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You may need to use the appropriate appendix table or technology to answer this question. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard.

You may need to use the appropriate appendix table or technology to answer this question. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 1GP
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#7 CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard.

#8. 

Consider the following hypothesis test.
H0: ? = 19
Ha: ? ≠ 19
A sample of 48 provided a sample mean 
x = 18
 and a sample standard deviation 
s = 4.4.
You may need to use the appropriate appendix table or technology to answer this question. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard. (a) Formulate the hypotheses for this application. Ho:μ ≥ 8 H < 8 H₁: μ = 8 H₂:μ # 8 Ho:μ ≤ 8 Ha: μ> 8 Hg: μ > 8 H₂:μ ≤ 8 н (d) Ho: μ< 8 Hg: μ 2 8 (b) A sample of 110 shoppers showed a sample mean waiting time of 8.4 minutes. Assume a population standard deviation of ♂ = 3.2 minutes. What is the test statistic? (Round your answer to two decimal places.) 1.31 What is the p-value? (Round your answer to four decimal places.) p-value = 0.1802 (c) At a = 0.05, what is your conclusion? Do not reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. O Do not reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Compute a 95% confidence interval for the population mean. (Round your answers to two decimal places.) 7.82 to 8.98 Does it support your conclusion? The confidence interval contains the hypothesized value of μ, therefore we do not reject ✓ Ho. The conclusion is the same as in part (c).
Transcribed Image Text:You may need to use the appropriate appendix table or technology to answer this question. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting time differs from this standard. (a) Formulate the hypotheses for this application. Ho:μ ≥ 8 H < 8 H₁: μ = 8 H₂:μ # 8 Ho:μ ≤ 8 Ha: μ> 8 Hg: μ > 8 H₂:μ ≤ 8 н (d) Ho: μ< 8 Hg: μ 2 8 (b) A sample of 110 shoppers showed a sample mean waiting time of 8.4 minutes. Assume a population standard deviation of ♂ = 3.2 minutes. What is the test statistic? (Round your answer to two decimal places.) 1.31 What is the p-value? (Round your answer to four decimal places.) p-value = 0.1802 (c) At a = 0.05, what is your conclusion? Do not reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Reject Ho. There is sufficient evidence to conclude that the population mean waiting time differs from 8 minutes. O Do not reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Reject Ho. There is insufficient evidence to conclude that the population mean waiting time differs from 8 minutes. Compute a 95% confidence interval for the population mean. (Round your answers to two decimal places.) 7.82 to 8.98 Does it support your conclusion? The confidence interval contains the hypothesized value of μ, therefore we do not reject ✓ Ho. The conclusion is the same as in part (c).
Consider the following hypothesis test. Ho: μ = 19 Ha: μ ‡ 19 A sample of 48 provided a sample mean x = 18 and a sample standard deviation s = 4.4. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) -1.575 (b) Use the t distribution table to compute a range for the p-value. p-value > 0.200 0.100 < p-value < 0.200 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 p-value < 0.010 (c) At a = 0.05, what is your conclusion? Reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Do not reject Ho. There is sufficient evidence to conclude that µ ‡ 19. ● Do not reject Hỏ. There is insufficient evidence to conclude that µ ‡ 19. Reject Ho. There is sufficient evidence to conclude that μ # 19. (d) What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.) test statistic ≤ 2.012 test statistic ≥ -2.012 X What is your conclusion? Reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Do not reject Ho. There is sufficient evidence to conclude that µ ‡ 19. ● Do not reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Reject Ho. There is sufficient evidence to conclude that µ ‡ 19.
Transcribed Image Text:Consider the following hypothesis test. Ho: μ = 19 Ha: μ ‡ 19 A sample of 48 provided a sample mean x = 18 and a sample standard deviation s = 4.4. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) -1.575 (b) Use the t distribution table to compute a range for the p-value. p-value > 0.200 0.100 < p-value < 0.200 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 p-value < 0.010 (c) At a = 0.05, what is your conclusion? Reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Do not reject Ho. There is sufficient evidence to conclude that µ ‡ 19. ● Do not reject Hỏ. There is insufficient evidence to conclude that µ ‡ 19. Reject Ho. There is sufficient evidence to conclude that μ # 19. (d) What is the rejection rule using the critical value? (If the test is one-tailed, enter NONE for the unused tail. Round your answer to three decimal places.) test statistic ≤ 2.012 test statistic ≥ -2.012 X What is your conclusion? Reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Do not reject Ho. There is sufficient evidence to conclude that µ ‡ 19. ● Do not reject Ho. There is insufficient evidence to conclude that µ ‡ 19. Reject Ho. There is sufficient evidence to conclude that µ ‡ 19.
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