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1.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.005.MI.S.

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A random sample of40binomial trials resulted in16successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(a) Can a normal distribution be used for thepdistribution? Explain. No,npandnqare both less than 5.Yes,npandnqare both greater than 5. No,npis greater than 5, butnqis less than 5.No,nqis greater than 5, butnpis less than 5.Yes,npandnqare both less than 5.

(b) State the hypotheses. H₀:p= 0.5;H₁:p< 0.5H₀:p= 0.5;H₁:p0.5 H₀:p< 0.5;H₁:p= 0.5H₀:p= 0.5;H₁:p> 0.5

(c) Computep. Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.) (d) Find theP-value of the test statistic. (Round your answer to four decimal places.) (e) Do you reject or fail to reject

H₀?

Explain. 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.

(f) What do the results tell you? The samplepvalue based on 40 trials is sufficiently different from 0.50 to not rejectH₀for= 0.05.The samplepvalue based on 40 trials is not sufficiently different from 0.50 to justify rejectingH₀for= 0.05. The samplepvalue based on 40 trials is not sufficiently different from 0.50 to not rejectH₀for= 0.05.The samplepvalue based on 40 trials is sufficiently different from 0.50 to justify rejectingH₀for= 0.05.

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2.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.007.S.

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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample ofn=222numerical entries from the file andr=51of the entries had a first nonzero digit of 1. Letprepresent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim thatpis less than 0.301. Use=0.05.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:p= 0.301;H₁:p> 0.301H₀:p< 0.301;H₁:p= 0.301 H₀:p= 0.301;H₁:p< 0.301H₀:p= 0.301;H₁:p0.301

(b) What sampling distribution will you use?The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp> 5 andnq> 5. The Student'st, sincenp< 5 andnq< 5.The standard normal, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find theP-value of the test statistic. (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 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. There is sufficient evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is less than 0.301.There is insufficient evidence at the 0.05 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is less than 0.301.

(ii) Ifpis in fact less than 0.301, would it make you suspect that there are not enough numbers in the data file with leading 1's? Could this indicate that the books have been "cooked" by "pumping up" or inflating the numbers? Comment from the viewpoint of a stockholder. Comment from the perspective of the Federal Bureau of Investigation as it looks for money laundering in the form of false profits.No. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts.Yes. The revenue data file seems to include more numbers with higher first nonzero digits than Benford's law predicts. Yes. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.No. The revenue data file does not seem to include more numbers with higher first nonzero digits than Benford's law predicts.

(iii) Comment on the following statement: If we reject the null hypothesis at level of significance, we have not provedH_oto be false. We can say that the probability isthat we made a mistake in rejectingH_o. Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?We have not provedH₀to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.We have not provedH₀to be false. Because our data lead us to reject the null hypothesis, more investigation is merited. We have not provedH₀to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.We have provedH₀to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.

3.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.009.S.

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Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of39arrests last month,26were of males aged 15 to 34 years. Use a10%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:p= 0 .7;H₁:p< 0.7H₀:p< 0 .7;H₁:p= 0.7 H₀:p= 0.7;H₁:p0.7H₀:p0.7;H₁:p= 0.7H₀:p= 0.7;H₁:p> 0.7

(b) What sampling distribution will you use?The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp< 5 andnq< 5. The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find theP-value of the test statistic. (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= 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. At the= 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the= 0.10 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.There is sufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.There is insufficient evidence at the 0.10 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.

4.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.010.MI.S.

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Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of36women athletes at the school showed that21eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a1% level of significance.

(a)

What is the level of significance?

(b)

State the null and alternate hypotheses.

H₀:p< 0.67;H₁:p= 0.67H₀:p= 0.67;H₁:p0.67 H₀:p= 0.67;H₁:p< 0.67H₀:p= 0.67;H₁:p> 0.67

What sampling distribution will you use?

The standard normal, sincenp> 5 andnq> 5.The standard normal, sincenp< 5 andnq< 5. The Student'st, sincenp> 5 andnq> 5.The Student'st, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)

Find theP-value of the test statistic. (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 between 1.11 and 3 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 between1.11 and 3 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 and1.11 as well as the area under the curve between 1.11 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 between3 and1.11 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 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 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.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.There is insufficient evidence at the 0.01 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

5.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.011.MI.S.

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The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of52records of automobile driver fatalities in a certain county showed that33involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use=0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:p= 0.77;H₁:p> 0.77H₀:p= 0.77;H₁:p< 0.77 H₀:p= 0.77;H₁:p0.77H₀:p< 0.77;H₁:p= 0.77

(b)

What sampling distribution will you use?

The standard normal, sincenp< 5 andnq< 5.The standard normal, sincenp> 5 andnq> 5. The Student'st, sincenp> 5 andnq> 5.The Student'st, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)

Find theP-value of the test statistic. (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 and2.32 as well as the area under the curve between 2.32 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 between2.32 and 3 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 and2.32 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 2.32 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= 0.05 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.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.There is insufficient evidence at the 0.05 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.

6.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.012.S.

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What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.Suppose a random sample ofn=60college students were surveyed andr=14of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use= 0.05.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:p= 0.24;H₁:p> 0.24H₀:p0.24;H₁:p= 0.24 H₀:p= 0.24;H₁:p< 0.24H₀:p= 0.24;H₁:p0.24

(b) What sampling distribution will you use?The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp> 5 andnq> 5. The standard normal, sincenp< 5 andnq< 5.The Student'st, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find theP-value of the test statistic. (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 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.There is sufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.There is insufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.

7.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.013.S.

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The following is based on information fromThe Wolf in the Southwest: The Making of an Endangered Species, by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of37wolves, there were only11females. One theory is that male wolves tend to return sooner than females to their old territories, where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use= 0.01.

(a) What is the level of significance? State the null and alternate hypotheses.H₀:p= 0.5;H₁:p> 0.5H₀:p< 0.5;H₁:p= 0.5 H₀:p= 0.5;H₁:p0.5H₀:p= 0.5;H₁:p< 0.5

(b) What sampling distribution will you use?The standard normal, sincenp< 5 andnq< 5.The Student'st, sincenp< 5 andnq< 5. The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp> 5 andnq> 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.) (c) Find theP-value of the test statistic. (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 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 fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.There is sufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.There is insufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.

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8.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.014.MI.S.

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In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer67out of a random sample of82guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use= 0.05.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:p0.75;H₁:p= 0.75H₀:p= 0.75;H₁:p0.75 H₀:p< 0.75;H₁:p= 0.75H₀:p= 0.75;H₁:p> 0.75H₀:p= 0.75;H₁:p< 0.75

(b)

What sampling distribution will you use?

The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp> 5 andnq> 5. The Student'st, sincenp< 5 andnq< 5.The standard normal, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)

Find theP-value of the test statistic. (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 and1.4 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 1.4 and 3 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 between1.4 and 3 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 and1.4 as well as the area under the curve between 1.4 and 3 are both 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 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.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.There is insufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.

9.

[-/0.3 Points]DETAILSBBUNDERSTAT12 8.3.016.MI.S.

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Symposiumis part of a larger work referred to as Plato'sDialogues. Wishart and Leachfound that about 21.4% of five-syllable sequences inSymposiumare of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is part of Plato'sDialogues. A random sample of494five-syllable sequences from this manuscript showed that129were of the type four short and one long. Do the data indicate that the population proportion of this type of five-syllable sequence is higher than that found in Plato'sSymposium? Use= 0.01.

(a)

What is the level of significance?

State the null and alternate hypotheses.

H₀:p< 0.214;H₁:p= 0.214H₀:p> 0.214;H₁:p= 0.214 H₀:p= 0.214;H₁:p0.214H₀:p= 0.214;H₁:p< 0.214H₀:p= 0.214;H₁:p> 0.214

(b)

What sampling distribution will you use?

The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp< 5 andnq< 5. The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)

Find theP-value of the test statistic. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the standard distribution 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 and1.55 is shaded.

A plot of the standard distribution 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 1.55 is shaded.

A plot of the standard distribution 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 2.55 and 4 is shaded.

A plot of the standard distribution 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 and1.55 as well as the area under the curve between 1.55 and 4 are both 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 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 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.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence is higher than that in Plato'sSymposium.There is insufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence is higher than that in Plato'sSymposium.