Question
8;4 1. [-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.003. MY NOTES ASK YOUR TEACHER When testing the difference of means for paired data, what is the null hypothesis? H
8;4
1.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.003.
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When testing the difference of means for paired data, what is the null hypothesis?Ho:d< 0Ho:d> 0 Ho:d= 0Ho:d0
2.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.009.MI.S.
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In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.
Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at rowB, the annual company percentage increase in revenue, versus rowA, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:
| B: Percent increase for company | 24 | 23 | 27 | 18 | 6 | 4 | 21 | 37 |
|---|---|---|---|---|---|---|---|---|
| A: Percent increase for CEO | 21 | 25 | 22 | 14 | 4 | 19 | 15 | 30 |
Do these data indicate that the population mean percentage increase in corporate revenue (rowB) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Letd=BA.)
(a)
What is the level of significance?
State the null and alternate hypotheses.
H0:d0;H1:d= 0H0:d> 0;H1:d= 0 H0:d= 0;H1:d> 0H0:d= 0;H1:d0H0:d= 0;H1:d< 0
(b)
What sampling distribution will you use? What assumptions are you making?
The Student'st. We assume thatdhas an approximately normal distribution.The Student'st. We assume thatdhas an approximately uniform distribution. The standard normal. We assume thatdhas an approximately normal distribution.The standard normal. We assume thatdhas an approximately uniform distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c)
Find (or estimate) theP-value.
P-value > 0.5000.250 <P-value < 0.500 0.100 <P-value < 0.2500.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010
Sketch the sampling distribution and show the area corresponding to theP-value.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.818 and 4 is shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and0.818 as well as the area under the curve between 0.818 and 4 are both shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and0.818 is shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between0.818 and 4 is shaded.
(d)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
Since theP-value, we fail to rejectH0. The data are statistically significant.Since theP-value >, we rejectH0. The data are not statistically significant. Since theP-value >, we fail to rejectH0. The data are not statistically significant.Since theP-value, we rejectH0. The data are statistically significant.
(e)
Interpret your conclusion in the context of the application.
Fail to rejectH0. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.Fail to rejectH0. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary. RejectH0. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.RejectH0. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.
3.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.010.S.
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In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer. Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let rowBrepresent hours per fish caught fishing from the shore, and let rowArepresent hours per fish caught using a boat. The following data are paired by month from October through April.
| Oct | Nov | Dec | Jan | Feb | March | April | |
| B: Shore | 1.5 | 1.7 | 2.1 | 3.2 | 3.9 | 3.6 | 3.3 |
| A: Boat | 1.4 | 1.5 | 1.5 | 2.2 | 3.3 | 3.0 | 3.8 |
Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Letd=BA.)(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?H0:d= 0;H1:d> 0; right-tailedH0:d= 0;H1:d0; two-tailed H0:d= 0;H1:d< 0; left-tailedH0:d0;H1:d= 0; two-tailed
(b) What sampling distribution will you use? What assumptions are you making?The Student'st. We assume thatdhas an approximately uniform distribution.The standard normal. We assume thatdhas an approximately uniform distribution. The Student'st. We assume thatdhas an approximately normal distribution.The standard normal. We assume thatdhas an approximately normal distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) theP-value. P-value > 0.5000.250 <P-value < 0.500 0.100 <P-value < 0.2500.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
(e) State your conclusion in the context of the application.Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.
4.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.011.S.
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In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.
| Weather Station | 1 | 2 | 3 | 4 | 5 |
| January | 135 | 122 | 128 | 64 | 78 |
| April | 104 | 113 | 100 | 88 | 61 |
Does this information indicate that the peak wind gusts are higher in January than in April? Use= 0.01. (Letd= JanuaryApril.)(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?H0:d= 0;H1:d< 0; left-tailedH0:d= 0;H1:d0; two-tailed H0:d> 0;H1:d= 0; right-tailedH0:d= 0;H1:d> 0; right-tailed
(b) What sampling distribution will you use? What assumptions are you making?The Student'st. We assume thatdhas an approximately normal distribution.The standard normal. We assume thatdhas an approximately normal distribution. The standard normal. We assume thatdhas an approximately uniform distribution.The Student'st. We assume thatdhas an approximately uniform distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) theP-value. P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January.Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January.
5.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.012.MI.S.
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In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.
The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To prevent car accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences. Although the fences prevent accidents, they also disturb the winter migration pattern of many animals. To compensate for this disturbance, the highways have frequent wilderness underpasses designed for exclusive use by deer, elk, and other animals.
In Colorado, there is a large group of deer that spend their summer months in a region on one side of a highway and survive the winter months in a lower region on the other side. To determine if the highway has disturbed deer migration to the winter feeding area, the following data were gathered on a random sample of 10 wilderness districts in the winter feeding area. RowBrepresents the average January deer count for a 5-year period before the highway was built, and rowArepresents the average January deer count for a 5-year period after the highway was built. The highway department claims that the January population has not changed. Test this claim against the claim that the January population has dropped. Use a 5% level of significance. Units used in the table are hundreds of deer. (Letd=BA.)
| Wilderness District | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| B: Before highway | 10.1 | 7.2 | 12.7 | 5.6 | 17.4 | 9.9 | 20.5 | 16.2 | 18.9 | 11.6 |
| A: After highway | 9.1 | 8.2 | 10.2 | 4.3 | 4.0 | 7.1 | 15.2 | 8.3 | 12.2 | 7.3 |
(a)
What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0:d> 0;H1:d= 0; right-tailedH0:d= 0;H1:d> 0; right-tailed H0:d= 0;H1:d< 0; left-tailedH0:d= 0;H1:d0; two-tailed
(b)
What sampling distribution will you use? What assumptions are you making?
The Student'st. We assume thatdhas an approximately uniform distribution.The standard normal. We assume thatdhas an approximately normal distribution. The standard normal. We assume thatdhas an approximately uniform distribution.The Student'st. We assume thatdhas an approximately normal distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c)
Find (or estimate) theP-value. (Round your answer to four decimal places.)
P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.0250.0005 <P-value < 0.005
Sketch the sampling distribution and show the area corresponding to theP-value.
A plot of the sampling distribution curve has a horizontal axis with values oft, 0, andtlabeled, wheretis to the left of 0 andtis to the right of 0. Two arrows, one pointing totand the other pointing totare labeledP-value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve to the left oftas well as the area under the curve to the right oftare both shaded.
A plot of the sampling distribution curve has a horizontal axis with values oftand 0 labeled, wheretis to the left of 0. An arrow pointing totis labeledP-value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve to the left oftis shaded.
A plot of the sampling distribution curve has a horizontal axis with values oftand 0 labeled, wheretis to the left of 0. An arrow pointing totis labeledP-value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve to the right oftis shaded.
A plot of the sampling distribution curve has a horizontal axis with values of 0 andtlabeled, wheretis to the right of 0. An arrow pointing totis labeledP-value. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve to the right oftis shaded.
(d)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
(e)
State your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence to claim that the January mean population of deer has dropped.Fail to reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer has dropped. Reject the null hypothesis, there is insufficient evidence to claim that the January mean population of deer has dropped.Reject the null hypothesis, there is sufficient evidence to claim that the January mean population of deer has dropped.
6.
[-/0.45 Points]DETAILSBBUNDERSTAT12 8.4.013.MI.S.
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In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedom d.f. not in the Student'st-table, use the closest d.f. that issmaller. In some situations, this choice of d.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.
In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below.
| Location of Wolf Pack | % Males (Winter) | % Males (Summer) |
|---|---|---|
| Finland | 76 | 59 |
| Finland | 35 | 40 |
| Finland | 79 | 63 |
| Lapland | 55 | 48 |
| Lapland | 64 | 55 |
| Russia | 50 | 50 |
| Russia | 41 | 50 |
| Russia | 55 | 45 |
It is hypothesized that in winter, "loner" males (not present in summer packs) join the pack to increase survival rate. Use a 5% level of significance to test the claim that the average percentage of males in a wolf pack is higher in winter. (Letd= wintersummer.)
(a)
What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H0:d> 0;H1:d= 0; right-tailedH0:d= 0;H1:d< 0; left-tailed H0:d= 0;H1:d> 0; right-tailedH0:d= 0;H1:d0; two-tailed
(b)
What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume thatdhas an approximately uniform distribution.The Student'st. We assume thatdhas an approximately normal distribution. The Student'st. We assume thatdhas an approximately uniform distribution.The standard normal. We assume thatdhas an approximately normal distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c)
Find (or estimate) theP-value.
P-value > 0.2500.125 <P-value < 0.250 0.100 <P-value < 0.1250.075 <P-value < 0.1000.050 <P-value < 0.075P-value < 0.050
Sketch the sampling distribution and show the area corresponding to theP-value.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.68 as well as the area under the curve between 1.68 and 4 are both shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and1.68 is shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.68 and 4 is shaded.
A plot of the sampling distribution probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between1.68 and 4 is shaded.
(d)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
(e)
State your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence to claim that the average percentage of male wolves in winter is higher.Fail to reject the null hypothesis, there is insufficient evidence to claim that the average percentage of male wolves in winter is higher. Reject the null hypothesis, there is insufficient evidence to claim that the average percentage of male wolves in winter is higher.Reject the null hypothesis, there is sufficient evidence to claim that the average percentage of male wolves in winter is higher.
part two 8'5
1.
[-/0.33 Points]DETAILSBBUNDERSTAT12 8.5.009.MI.S.
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A random sample of 49 measurements from one population had a sample mean of18, with sample standard deviation5. An independent random sample of64 measurementsfrom a second population had a sample mean of21, with sample standarddeviation6.Test the claim that the population means are different. Use level of significance 0.01.
(a) What distribution does the sample test statistic follow? Explain. The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
(b) State the hypotheses. H0:1=2;H1:1<2H0:1=2;H1:1>2 H0:1=2;H1:12H0:12;H1:1=2
(c) Compute
x1x2.
x1x2=
Compute the corresponding sample distribution value. (Test the difference12. Round your answer to three decimal places.) (d) Estimate theP-value of the sample test statistic. P-value > 0.5000.250 <P-value < 0.500 0.100 <P-value < 0.2500.050 <P-value < 0.1000.010 <P-value < 0.050P-value < 0.010
(e) Conclude the test. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret the results. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Reject the null hypothesis, there is sufficient evidence that there is a difference between the population means. Reject the null hypothesis, there is insufficient evidence that there is a difference between the population means.Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between the population means.
2.
[-/0.33 Points]DETAILSBBUNDERSTAT12 8.5.013.MI.S.
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For one binomial experiment,
n1= 75
binomial trials produced
r1=45
successes. For a second independent binomial experiment,
n2= 100
binomial trials produced
r2=65
successes.At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.
(a)
Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)
(b)
Check Requirements: What distribution does the sample test statistic follow? Explain.
The Student'st. The number of trials is sufficiently large.The standard normal. We assume the population distributions are approximately normal. The Student'st. We assume the population distributions are approximately normal.The standard normal. The number of trials is sufficiently large.
(c)
State the hypotheses.
H0:p1=p2;H1:p1p2H0:p1<p2;H1:p1=p2 H0:p1=p2;H1:p1<p2H0:p1=p2;H1:p1>p2
(d)
Computep1p2.
p1p2=
Compute the corresponding sample distribution value. (Test the differencep1p2. Do not use rounded values. Round your final answer to two decimal places.)
(e)
Find theP-value of the sample test statistic. (Round your answer to four decimal places.)
(f)
Conclude the test.
At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
(g)
Interpret the results.
Reject the null hypothesis, there is insufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.Fail to reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ. Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.Reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.
3.
[-/0.33 Points]DETAILSBBUNDERSTAT12 8.5.015.
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REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample ofn1=8children (9 years old) showed that they had an average REM sleep time ofx1=2.9hours per night. From previous studies, it is known that1=0.6hour. Another random sample ofn2=8adults showed that they had an average REM sleep time ofx2=2.10hours per night. Previous studies show that2=0.7hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.(a) What is the level of significance? State the null and alternate hypotheses.H0:1=2;H1:1<2H0:1=2;H1:12 H0:1=2;H1:1>2H0:1<2;H1:1=2
(b) What sampling distribution will you use? What assumptions are you making?The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults.
4.
[-/0.33 Points]DETAILSBBUNDERSTAT12 8.5.016.MI.
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A random sample ofn1=18winter days in Denver gave a sample mean pollution indexx1=43. Previous studies show that1=15. For Englewood (a suburb of Denver), a random sample ofn2=10winter days gave a sample mean pollution index ofx2=38. Previous studies show that2=13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance.
(a)
What is the level of significance?
State the null and alternate hypotheses.
H0:1=2;H1:1>2H0:1=2;H1:1<2 H0:1<2;H1:1=2H0:1=2;H1:12
(b)
What sampling distribution will you use? What assumptions are you making?
The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to two decimal places.)
(c)
Find (or estimate) theP-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and0.92 is shaded.
A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and0.92 as well as the area under the curve between 0.92 and 3 are both shaded.
A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between0.92 and 0.92 is shaded.
A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.92 and 3 is shaded.
(d)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e)
Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
5.
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A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample ofn1=46adults were asked about fishing as an outdoor activity. The mean response wasx1=4.9. Another random sample ofn2=48adults were asked about camping as an outdoor activity. For this group, the mean response wasx2=5.7. From previous studies, it is known that1=1.8and2=1.5. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance. Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement.(a) What is the level of significance? State the null and alternate hypotheses.H0:1=2;H1:1<2H0:1=2;H1:12 H0:1=2;H1:1>2H0:12;H1:1=2
(b) What sampling distribution will you use? What assumptions are you making?The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.Fail to reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing.Reject the null hypothesis, there is insufficient evidence that there is a difference between mean response regarding preference for camping or fishing. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing.Reject the null hypothesis, there is sufficient evidence that there is a difference between mean response regarding preference for camping or fishing.
6.
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Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken inn1=33U.S. cities. The sample mean for these cities showed thatx1=15.2%of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken inn2=34U.S. cities. The sample mean for these cities showed thatx2=17.8%of the young adults had attended college. From previous studies, it is known that1=6.6%and2=4.2%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use= 0.05.(a) What is the level of significance? State the null and alternate hypotheses.H0:1<2;H1:1=2H0:1=2;H1:1>2 H0:1=2;H1:1<2H0:1=2;H1:12
(b) What sampling distribution will you use? What assumptions are you making?The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with known standard deviations. The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to two decimal places.) (c) Find (or estimate) theP-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.Reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.Fail to reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher. Fail to reject the null hypothesis, there is insufficient evidence that the mean percentage of young adults who attend college is higher.Reject the null hypothesis, there is sufficient evidence that the mean percentage of young adults who attend college is higher.
7.
[-/0.33 Points]DETAILSBBUNDERSTAT12 8.5.019.MI.S.
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A random sample ofn1= 10 regions in New England gave the following violent crime rates (per million population).
| 3.5 | 3.9 | 4.2 | 4.1 | 3.3 | 4.1 | 1.8 | 4.8 | 2.9 | 3.1 |
Another random sample ofn2= 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).
| 3.5 | 4.3 | 4.5 | 5.5 | 3.3 | 4.8 | 3.5 | 2.4 | 3.1 | 3.5 | 5.2 | 2.8 |
Assume that the crime rate distribution is approximately normal in both regions.
(a)
Use a calculator to calculatex1,s1,x2, ands2. (Round your answers to four decimal places.)
x1=s1=x2=s2=
(b)
Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use= 0.01.
(i)
What is the level of significance?
State the null and alternate hypotheses.
H0:1=2;H1:1<2H0:1<2;H1:1=2 H0:1=2;H1:1>2H0:1=2;H1:12
(ii)
What sampling distribution will you use? What assumptions are you making?
The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to three decimal places.)
(iii)
Find (or estimate) theP-value.
P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005
Sketch the sampling distribution and show the area corresponding to theP-value.
A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between0.76 and 4 is shaded.
A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and 0.76 is shaded.
A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and0.76 is shaded.
A plot of the Student's t-probability curve has a horizontal axis with values from4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between4 and0.76 as well as the area under the curve between 0.76 and 4 are both shaded.
(iv)
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?
At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(v)
Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.Reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England. Fail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.Reject the null hypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than in New England.
8.
[-/0.39 Points]DETAILSBBUNDERSTAT12 8.5.020.S.
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A random sample ofn1= 16 communities in western Kansas gave the following information for people under 25 years of age.x1: Rate of hay fever per 1000 population for people under 25
| 100 | 92 | 122 | 129 | 94 | 123 | 112 | 93 |
| 125 | 95 | 125 | 117 | 97 | 122 | 127 | 88 |
A random sample ofn2= 14 regions in western Kansas gave the following information for people over 50 years old.x2: Rate of hay fever per 1000 population for people over 50
| 96 | 112 | 99 | 95 | 111 | 88 | 110 |
| 79 | 115 | 100 | 89 | 114 | 85 | 96 |
(i) Use a calculator to calculatex1,s1,x2, ands2. (Round your answers to four decimal places.)
| x1 | = |
| s1 | = |
| x2 | = |
| s2 | = |
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use= 0.05. (a) What is the level of significance? State the null and alternate hypotheses.H0:1=2;H1:1>2H0:1=2;H1:12 H0:1>2;H1:1=2H0:1=2;H1:1<2
(b) What sampling distribution will you use? What assumptions are you making?The standard normal. We assume that both population distributions are approximately normal with known standard deviations.The Student'st. We assume that both population distributions are approximately normal with unknown standard deviations. The Student'st. We assume that both population distributions are approximately normal with known standard deviations.The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
What is the value of the sample test statistic? (Test the difference12. Round your answer to three decimal places.) (c) Find (or estimate) theP-value. P-value > 0.2500.125 <P-value < 0.250 0.050 <P-value < 0.1250.025 <P-value < 0.0500.005 <P-value < 0.025P-value < 0.005
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.Reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age group over 50.Fail to reject the null hypothesis, there is sufficient evidence that the mean rate of hay fever is lower for the age grou
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Complex Analysis
Authors: Dennis G Zill, Patrick D Shanahan
3rd Edition
1449694624, 9781449694623
