Question 1

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9,the population the president is interested in is
A)all entering students to all universities in the United States this year.
B)all entering students to his university this year.
C)all SAT test centers in the United States this year.
D)the SAT scores of all students entering universities in the United States this year.

Accepted Answer

The president is specifically interested in his university's entering class this year and their SAT scores. Therefore, the population of interest is all entering students to his university this year.

Question 2

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,the lowest level of significance at which the null hypothesis can be rejected is ________.

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 3

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9,what critical value should the president use to determine the rejection region?

Accepted Answer

The answer of TABLE 9-9
The president of a university claimed...

Question 4

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,what will be the p-value if these data were used to perform a two-tail test?

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 5

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,the largest level of significance at which the null hypothesis will not be rejected is ________.

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 6

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-True or False: Referring to Table 9-9,the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Accepted Answer

The question does not provide information about the critical value or the test statistic for the hypothesis test. Therefore, it is not possible to determine whether the null hypothesis would be rejected at a 1% level of significance.

Question 7

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9,state the alternative hypothesis for this study.

Accepted Answer

The answer of TABLE 9-9
The president of a university claimed...

Question 8

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-True or False: Referring to Table 9-8,the null hypothesis would be rejected.

Accepted Answer

The null hypothesis states that there is no increase in the conversion rate, meaning the conversion rate remains at 10.1%. In the sample, 24 out of 200 browsers made a purchase, which is a conversion rate of 12%. To determine if this is statistically significant, a hypothesis test is needed. Without performing the test, we cannot conclude that the null hypothesis would be rejected.

Question 9

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,state the alternative hypothesis for this study.

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 10

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9,state the null hypothesis for this study.

Accepted Answer

The answer of TABLE 9-9
The president of a university claimed...

Question 11

TABLE 9-7
A major home improvement store conducted its biggest brand recognition campaign in the company's history.A series of new television advertisements featuring well-known entertainers and sports figures were launched.A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot".A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%.Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance.
-Referring to Table 9-7,what will be the p-value if these data were used to perform a two-tail test?

Accepted Answer

The answer of TABLE 9-7
A major home improvement store conducted...

Question 12

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,the parameter the company officials are interested in is
A)the mean number of browsers who buy something in their visit to the company's website.
B)the total number of browsers who buy something in their visit to the company's website.
C)the mean number of company officials who buy something in their visit to the company's website.
D)the proportion of browsers who buy something in their visit to the company's website.

Accepted Answer

The parameter the company officials are interested in is the proportion of browsers who buy something in their visit to the company's website. This is evident from the definition of "conversion rate" in the question, which is the percentage of browsers who buy something in their visit to a site. The conversion rate is measured in terms of proportions and not in terms of means or totals, so options A and B are incorrect. Option C is irrelevant and does not relate to the question at all. Therefore, the best choice is D, the proportion of browsers who buy something in their visit to the company's website.

Question 13

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-Referring to Table 9-9,the parameter the president is interested in is
A)the mean number of entering students to his university this year.
B)the mean number of entering students to all U.S.universities this year.
C)the mean SAT score of the entering students to his university this year.
D)the mean SAT score of the entering students to all U.S.universities this year.

Accepted Answer

The parameter the president is interested in is the mean SAT score of the entering students to his university this year. This is indicated by the fact that he compared it to the previous years' mean SAT score for entering students at his university. The other answer choices are not relevant to the question.

Question 14

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,the null hypothesis will be rejected if the test statistic is
A)greater than 1.645.
B)less than 1.645.
C)greater than -1.645.
D)less than -1.645.

Accepted Answer

To test the null hypothesis that there is no significant increase in conversion rate after the website redesign, a one-tailed z-test can be used with the following formula:

z = (p - P) / sqrt(P(1-P)/n)

where p is the sample proportion (24/200 = 0.12), P is the hypothesized proportion (10.1% or 0.101), and n is the sample size (200).

Plugging in these values, we get:

z = (0.12 - 0.101) / sqrt(0.101(1-0.101)/200) = 2.023

Since this is greater than the critical z-value of 1.645 for a one-tailed test at the 5% level of significance (as shown in Table 9-8), we reject the null hypothesis and conclude that there is evidence of an increase in conversion rate at the 5% level of significance.

Question 15

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,state the null hypothesis for this study.

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 16

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-True or False: Referring to Table 9-8,the value of the probability of committing a Type II error β is 0.95.

Accepted Answer

Table 9-8 is not given, so we cannot determine the value of β from the information provided in the question.

Question 17

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-True or False: Referring to Table 9-9,the null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

Accepted Answer

If a 10% probability of committing a Type I error is allowed, the significance level is higher than the 5% level. This means the critical value for rejection is less stringent, making it more likely to reject the null hypothesis.

Question 18

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-True or False: Referring to Table 9-8,the company officials can conclude that there is sufficient evidence that the conversion rate at the company's website has increased using a level of significance of 0.05.

Accepted Answer

The sample conversion rate is 24/200 = 12%. To determine if this is a significant increase from 10.1%, a hypothesis test is needed. The null hypothesis is that the conversion rate is still 10.1%. Using a significance level of 0.05, a statistical test (such as a z-test for proportions) would be conducted. Without performing the actual calculations, we cannot conclude if the increase is statistically significant.

Question 19

TABLE 9-8
One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate,the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.
-Referring to Table 9-8,what critical value should the company officials use to determine the rejection region?

Accepted Answer

The answer of TABLE 9-8
One of the biggest issues facing...

Question 20

TABLE 9-9
The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance.
-True or False: Referring to Table 9-9,the null hypothesis would be rejected.

Accepted Answer

To determine if the null hypothesis is rejected, a hypothesis test must be conducted. The null hypothesis is that the mean SAT score of this year's entering class is equal to or greater than previous years (1,520). Using a t-test for the sample mean (1,501) with a standard deviation of 53 and a sample size of 20, the calculated t-value must be compared to the critical t-value at a 5% significance level. The calculated t-value does not exceed the critical t-value, so the null hypothesis is not rejected.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests