1.)Use the given statement to represent a claim. Write its complement and state which is H0 and...
Question:
1.)Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha.
14
Find the complement of the claim.
less than or equals
not equals
less than<
equals=
greater than or equals
greater than>
14
Which is H0 and which is Ha?
A.
H0: 14
Ha: 14
B.
H0: 14
Ha: 14
C.
H0: 14
Ha: <14
D.
H0: <14
Ha: 14
E.
H0: 14
Ha: >14
F.
H0: 14
Ha: 14
G.
H0: 14
Ha: =14
H.
H0: 14
Ha: 14
I.
H0: =14
Ha:
2.)Find the minimum sample size n needed to estimate for the given values of c, , and E.
c=0.95, =6.9, and E=1
Assume that a preliminary sample has at least 30 members.
n=_______enter your response here (Round up to the nearest whole number.)
3.)Assume the random variable x is normally distributed with mean =50 and standard deviation =7. Find the indicated probability.
P(x>37)
P(x>37)=_____enter your response here
(Round to four decimal places as needed.)
4.)Find the indicated z-scores shown in the graph.
Click to view page 1 of the Standard Normal Table. LOADING...
Click to view page 2 of the Standard Normal Table. LOADING...
z=?
z=?
0
x
0.4706
0.4706
A normal curve is over a horizontal x-axis and is centered on 0. Vertical line segments extend from the curve to the horizontal axis at two points labeled z = ? each. The area under the curve between the left vertical line segment and 0 is shaded and labeled 0.4706. The area under the curve between 0 and the right vertical line segment is shaded and labeled 0.4706.
The z-scores are enter your response here.
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
5.)A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 917 milligrams. A random sample of 45 breakfast sandwiches has a mean sodium content of 910 milligrams. Assume the population standard deviation is 23 milligrams. At =0.05, do you have enough evidence to reject the restaurant's claim? Complete parts (a) through (e).
(a) Identify the null hypothesis and alternative hypothesis.
A.
H0: 917 (claim)
Ha: =917
B.
H0: >917
Ha: 917 (claim)
C.
H0: <910 (claim)
Ha: 910
D.
H0: 910
Ha: <910 (claim)
E.
H0: =910 (claim)
Ha: 910
F.
H0: 917 (claim)
Ha: >917
(b) Identify the critical value(s). Use technology.
z0=enter your response here
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Identify the rejection region(s). Select the correct choice below.
A.
The rejection regions are z>1.64 and z<1.64.
B.
The rejection region is z<1.64.
C.
The rejection region is z>1.64.
(c) Identify the standardized test statistic. Use technology.
z=enter your response here (Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A.
Fail to reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 917 milligrams.
B.
Reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 917 milligrams.
C.
Fail to reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 917 milligrams.
D.
Reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 917 milligrams.
6.)Use the confidence interval to find the margin of error and the sample mean.
(1.60,1.98)
The margin of error is______enter your response here.
(Round to two decimal places as needed.)
The sample mean is________ enter your response here.
(Type an integer or a decimal.)
7.)A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 746 hours. A random sample of 27 light bulbs has a mean life of 732 hours. Assume the population is normally distributed and the population standard deviation is 56 hours. At =0.05, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).
(a) Identify the null hypothesis and alternative hypothesis.
A.
H0: 746(claim)
Ha: =746
B.
H0: =732
Ha: 732 (claim)
C.
H0: 746 (claim)
Ha: <746
D.
H0: <732 (claim)
Ha: 732
E.
H0: >746
Ha: 746 (claim)
F.
H0: 732
Ha: >732 (claim)
(b) Identify the critical value(s). Use technology.
z0=enter your response here
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Identify the rejection region(s). Choose the correct answer below.
A.
-4
0
4
z
Reject H0.Reject H0.Fail to reject H0.
A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 1.6 and 1.6. The area under the curve to the left of negative 1.6 is shaded and the area under the curve to the right of 1.6 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.6 and 1.6 is shaded another color and labeled Fail to reject Upper H 0.
B.
-4
0
4
z
Reject H0.Fail to reject H0.
A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at negative 1.6. The area under the curve to the left of negative 1.6 is shaded one color and labeled Reject Upper H 0. The area under the curve to the right of negative 1.6 is shaded another color and labeled Fail to reject Upper H 0.
C.
-4
0
4
z
Reject H0.Fail to reject H0.
A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 1.6. The area under the curve to the right of 1.6 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.6 is shaded another color and labeled Fail to reject Upper H 0.
(c) Identify the standardized test statistic. Use technology.
z=enter your response here (Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
A.
Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 746 hours.
B.
Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 746 hours.
C.
Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 746 hours.
D.
Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 746 hours.
8.)A random sample of 75 eighth grade students' scores on a national mathematics assessment test has a mean score of 279. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 36. At =0.04, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).
(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.
A.
H0: 270 (claim)
Ha: >270
B.
H0: 270 (claim)
Ha: <270
C.
H0: =270 (claim)
Ha: >270
D.
H0: <270
Ha: 270 (claim)
E.
H0: 270
Ha: >270 (claim)
F.
H0: =270
Ha: >270 (claim)
(b) Find the standardized test statistic z, and its corresponding area.
z=enter your response here (Round to two decimal places as needed.)
(c) Find the P-value.
P-value=enter your response here (Round to three decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Fail to reject H0
Reject H0
(e) Interpret your decision in the context of the original claim.
At the 4% significance level, there
is
is not
enough evidence to
support
reject
the administrator's claim that the mean score for the state's eighth graders on the exam is more than 270.
9.)Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance .
Right-tailed test with test statistic z=1.18 and =0.08
P-value=enter your response here (Round to four decimal places as needed.)
State your conclusion.
Reject H0
Fail to reject
10.)The mean height of women in a country (ages 2029) is 64.3 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume =2.83.
The probability that the mean height for the sample is greater than 65 inches is______ enter your response here.
(Round to four decimal places as needed.)
11.)Find the critical value(s) for a left-tailed z-test with =0.06. Include a graph with your answer.
The critical value(s) is(are) enter your response here.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Draw a graph of the rejection region. Choose the correct graph below.
A.
-3
0
3
z
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the right of the vertical line segment is shaded and labeled .
B.
-3
0
3
z
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the vertical line segment is shaded and labeled .
C.
-3
0
3
z
1
2
1
2
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right of 0 from the horizontal axis to the curve. The area under the curve to the left of and to the right of the vertical line segments is shaded and labeled @DIV{1;2}.
D.
-3
0
3
z
12.)Find the indicated probability using the standard normal distribution.
P(z>1.37)
Click here to view page 1 of the standard normal table. LOADING...
Click here to view page 2 of the standard normal table. LOADING...
P(z>1.37)=_____enter your response here (Round to four decimal places as needed.)
13.)Use the normal distribution of SAT critical reading scores for which the mean is 512 and the standard deviation is 119. Assume the variable x is normally distributed.
(a)
What percent of the SAT verbal scores are less than 675?
(b)
If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 525?
(a) Approximately___ enter your response here% of the SAT verbal scores are less than 675.
(Round to two decimal places as needed.)
(b) You would expect that approximately____enter your response here SAT verbal scores would be greater than 525. (Round to the nearest whole number as needed.)
14.)Find the critical value zc necessary to form a confidence interval at the level of confidence shown below.
c=0.94
zc=____enter your response here
(Round to two decimal places as needed.)
15.)Find the margin of error for the given values of c, , and n.
c=0.90, =3.9, n=81
LOADING... Click the icon to view a table of common critical values.
E=____enter your response here (Round to three decimal places as needed.)
16.)State whether the standardized test statistic z indicates that you should reject the null hypothesis.
(a) z=1.364
(b) z=1.137
(c) z=1.113
(d) z=1.495
-4
0
4
z
z0=1.285
A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve at z 0 equals 1.285 . The area under the curve to the right of z 0 equals 1.285 is shaded.
(a) For zequals=1.3641.364, should you reject or fail to reject the null hypothesis?
A.
RejectReject Upper H 0H0 because z greater than 1.285z>1.285.
B.
Fail to rejectFail to rejectUpper H 0H0 because z greater than 1.285z>1.285.
C.
RejectReject Upper H 0H0 because z less than 1.285z<1.285.
D.
Fail to rejectFail to reject Upper H 0H0 because z less than 1.285z<1.285.
(b) For zequals=1.1371.137, should you reject or fail to reject the null hypothesis?
A.
RejectReject Upper H 0H0 because z less than 1.285z<1.285.
B.
RejectReject Upper H 0H0 because z greater than 1.285z>1.285.
C.
Fail to rejectFail to reject Upper H 0H0 because z less than 1.285z<1.285.
D.
Fail to rejectFail to reject Upper H 0H0 because z greater than 1.285z>1.285.
(c) For zequals=negative 1.1131.113, should you reject or fail to reject the null hypothesis?
A.
RejectReject Upper H 0H0 because z less than 1.285z<1.285.
B.
Fail to rejectFail to reject Upper H 0H0 because z greater than 1.285z>1.285.
C.
RejectReject Upper H 0H0 because z greater than 1.285z>1.285.
D.
Fail to rejectFail to reject Upper H 0H0 because z less than 1.285z<1.285.
(d) For zequals=1.4951.495, should you reject or fail to reject the null hypothesis?
A.
Fail to rejectFail to reject Upper H 0H0 because z greater than 1.285z>1.285.
B.
RejectReject Upper H 0H0 because z less than 1.285z<1.285.
C.
Fail to rejectFail to reject Upper H 0H0 because z less than 1.285z<1.285.
D.
RejectReject Upper H 0H0 because z greater than 1.285z>1.285.
17.)Find the critical value(s) for a left-tailed z-test with =0.05. Include a graph with your answer.
The critical value(s) is(are)____ enter your response here.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Draw a graph of the rejection region. Choose the correct graph below.
A.
-3
0
3
z
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the vertical line segment is shaded and labeled .
B.
-3
0
3
z
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the left of the vertical line segment is shaded and labeled .
C.
-3
0
3
z
1
2
1
2
A normal curve is over a horizontal axis labeled z from negative 3.5 to 3.5 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right of 0 from the horizontal axis to the curve. The area under the curve to the left of and to the right of the vertical line segments is shaded and labeled @DIV{1;2}.
D.
-3
0
3
z
18.)Find the critical value(s) and rejection region(s) for the type of z-test with level of significance . Include a graph with your answer.
Right-tailed test, =0.01
The critical value(s) is/are z=enter your response here.
(Round to two decimal places as needed. Use a comma to separate answers as needed.)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Round to two decimal places as needed.)
A.
The rejection region is z>enter your response here.
B.
The rejection region is z C. The rejection regions are z Choose the correct graph of the rejection region below. A. 0zz A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative z, 0 and z, where negative z is to the left of 0 and z is to the right of 0. The area under the curve to the left of negative z and to the right of z is shaded. B. 0 z A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at 0 and z, where z is to the right of 0. The area under the curve to the right of z is shaded. C. 0zz A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative z, 0 and z, where negative z is to the left of 0 and z is to the right of 0. The area under the curve between negative z and z is shaded. D. 0 z A normal curve is over a horizontal axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at 0 and z, where z is to the right of 0. The area under the curve to the left of z is shaded. 19.)The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0when the level of significance is (a) =0.01, (b) =0.05, and (c) =0.10. P=0.0134 (a) Do you reject or fail to reject H0 at the 0.01 level of significance? A. Reject H0 because the P-value, 0.0134, is less than =0.01. B. RejectH0 because the P-value, 0.0134, is greater than =0.01. C. Fail to reject H0 because the P-value, 0.0134, is greater than =0.01. D. Fail to reject H0 because the P-value, 0.0134, is less than =0.01. (b) Do you reject or fail to reject H0 at the 0.05 level of significance? A. Fail to reject H0 because the P-value, 0.0134, is greater than =0.05. B. Reject H0 because the P-value, 0.0134, is less than =0.05. C. Reject H0 because the P-value, 0.0134, is greater than =0.05. D. Fail to reject H0 because the P-value, 0.0134, is less than =0.05. (c) Do you reject or fail to reject H0 at the 0.10 level of significance? A. Fail to reject H0 because the P-value, 0.0134, is less than =0.10. B. Reject H0 because the P-value, 0.0134, is greater than =0.10. C. Fail to reject H0 because the P-value, 0.0134, is greater than =0.10. D. Reject H0 because the P-value, 0.0134, is less than =0.10. 20.)Find the indicated area under the standard normal curve. Between z=2.32 and z=2.32 Click here to view page 1 of the standard normal table. LOADING... Click here to view page 2 of the standard normal table. LOADING... The area between z=2.32 and z=2.32 under the standard normal curve is____ enter your response here. (Round to four decimal places as needed.) 21.)Use the standard normal table to find the z-score that corresponds to the cumulative area 0.1635 0.1635. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. Click to view page 1 of the standard normal table. LOADING... Click to view page 2 of the standard normal table. LOADING... z equals = enter your response here (Type an integer or decimal rounded to three decimal places as needed.) 22.)A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. H0: 2.6 Ha: < 2.6 What type of test is being conducted in this problem? A. Left-tailed test B. Two-tailed test C. Right-tailed test 23.)The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $14. Find the probability that a randomly selected utility bill is (a) less than $69, (b) between $87 and $120, and (c) more than $140. (a) The probability that a randomly selected utility bill is less than $69 is___enter your response here. (Round to four decimal places as needed.) (b) The probability that a randomly selected utility bill is between $87 and $120 is_____ enter your response here. (Round to four decimal places as needed.) (c) The probability that a randomly selected utility bill is more than $140 is____ enter your response here. (Round to four decimal places as needed.) 24.)Use the normal distribution of SAT critical reading scores for which the mean is 511 and the standard deviation is 110. Assume the variable x is normally distributed. (a) What percent of the SAT verbal scores are less than 650? (b) If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 550? (a) Approximately___ enter your response here% of the SAT verbal scores are less than 650. (Round to two decimal places as needed.) (b) You would expect that approximately___ enter your response here SAT verbal scores would be greater than 550. (Round to the nearest whole number as needed.) 25.)A nutritionist claims that the mean tuna consumption by a person is 3.6 pounds per year. A sample of 50 people shows that the mean tuna consumption by a person is 3.4 pounds per year. Assume the population standard deviation is 1.17 pounds. At =0.03, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. A. H0: =3.6 Ha: 3.6 B. H0: >3.6 Ha: 3.6 C. H0: 3.4 Ha: >3.4 D. H0: >3.4 Ha: 3.4 E. H0: 3.6 Ha: >3.6 F. H0: 3.4 Ha: =3.4 (b) Identify the standardized test statistic. z=___enter your response here (Round to two decimal places as needed.) (c) Find the P-value._____ enter your response here (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. A. Reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.6 pounds. B. Reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.6 pounds. C. Fail to reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.6 pounds. D. Fail to reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.6 pounds.
Expert Answer:
