Question

A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average. A random sample of 25 five-person families in San Antonio showed a mean of $133.47 and a standard deviation of $11.19. Assume that the national average weekly grocery bill for a five-person family is $129. Does the sample result provide convincing evidence that the mean weekly grocery bill of a five-person family in San Antonio is different from the national average? To answer this question, you decide to run a 2-sided test. To answer this question, please complete the following grid (you can copy and paste it into Blackboard). Test to be performed (Z vs t test). Explain your answer. Null and Alternative hypothesis (i.e. Ho: Ha: ) Critical value (3 decimal points) Test statistic (3 decimal points) [show equation and answer] p-value for the test statistic (3 decimal points). Describe in words what this p-value means using language specific to this problem. Decision (reject Ho in favor of Ha, fail to reject Ho) Which decision criterion (CI, p-value or critical t) did you use to make a decision? Define your rejection zone using the chosen criterion and describe how you used it to make your decision. (Be specific in your answer to this problem) Describe your decision in words (i.e. what would you report back to your key stakeholders about your findings). Name one general category of key stakeholder that might be interested in this information and why (i.e. how might they use this information to influence their business or policy decision making? (only need to list 1 key stakeholder; 1-2 lines should suffice for explanation) At the 99% confidence level, what numerical values of the hypothesized mean $\mu_0$ would allow you to conclude that you could reject Ho in favor of Ha?

A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average. A
random sample of 25 five-person families in San Antonio showed a mean of $133.47 and a standard deviation of $11.19.
Assume that the national average weekly grocery bill for a five-person family is $129. Does the sample result provide convincing evidence that the mean weekly
grocery bill of a five-person family in San Antonio is different from the national average? To answer this question, you decide to run a 2-sided test.
To answer this question, please complete the following grid (you can copy and paste it into Blackboard).
Test to be performed (Z vs t test). Explain your answer.
Null and Alternative hypothesis (i.e. Ho: Ha: )
Critical value (3 decimal points)
Test statistic (3 decimal points) [show equation and answer]
p-value for the test statistic (3 decimal points). Describe in words
what this p-value means using language specific to this problem.
Decision (reject Ho in favor of Ha, fail to reject Ho)
Which decision criterion (CI, p-value or critical t) did you use to
make a decision? Define your rejection zone using the chosen
criterion and describe how you used it to make your decision.
(Be specific in your answer to this problem)
Describe your decision in words (i.e. what would you report back
to your key stakeholders about your findings).
Name one general category of key stakeholder that might be
interested in this information and why (i.e. how might they use
this information to influence their business or policy decision
making? (only need to list 1 key stakeholder; 1-2 lines should
suffice for explanation)
At the 99% confidence level, what numerical values of the
hypothesized mean $\mu_0$ would allow you to conclude that you
could reject Ho in favor of Ha?

Added by Curtis M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/08/2023

Step 1

Explain your answer. Since we are comparing the mean of a sample to a known population mean, we will use a t-test in this case. This is because the population standard deviation is not known and we are using the sample standard deviation to estimate it. Show more…

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A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average. A random sample of 25 five-person families in San Antonio showed a mean of $133.47 and a standard deviation of $11.19. Assume that the national average weekly grocery bill for a five-person family is $129. Does the sample result provide convincing evidence that the mean weekly grocery bill of a five-person family in San Antonio is different from the national average? To answer this question, you decide to run a 2-sided test. To answer this question, please complete the following grid (you can copy and paste it into Blackboard). A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average. A random sample of 25 five-person families in San Antonio showed a mean of $133.47 and a standard deviation of $11.19. Assume that the national average weekly grocery bill for a five-person family is $129.Does the sample result provide convincing evidence that the mean weekly grocery bill of a five-person family in San Antonio is different from the national average? To answer this question,you decide to run a 2-sided test. To answer this question,please complete the following grid (you can copy and paste it into Blackboard). Test to be performed (Z vs t test). Explain your answer. Null and Alternative hypothesis (i.e. Ho: Ha: Critical value (3 decimal points) Test statistic (3 decimal points) [show equation and answer] p-value for the test statistic (3 decimal points).Describe in words what this p-value means using language specific to this problem. Decision reject Ho in favor of Ha,fail to reject Ho Which decision criterion (Ci, p-value or critical t) did you use to make a decision? Define your rejection zone using the chosen criterion and describe how you used it to make your decision. (Be specific in your answer to this problem) Describe your decision in words (i.e. what would you report back to your key stakeholders about your findings). Name one general category of key stakeholder that might be interested in this information and why (i.e. how might they use this information to influence their business or policy decision making? (only need to list 1 key stakeholder; 1-2 lines should suffice for explanation) At the 99% confidence level, what numerical values of the hypothesized mean o would allow you to conclude that you could reject Ho in favor of Ha?