A cell phone company knows that the mean length of calls for all of its customers in a certain city is 9.3 minutes. The company is thinking about offering a senior discount to attract new customers, but only wants to do so if the mean length of calls for current customers who are seniors (65 and over) is lower than it is for the general customer pool. The only way to identify seniors is to conduct a survey and ask people whether they are over age 65. Using this method, the company contacts a random sample of 100 seniors and records the length of their last call. The sample mean and standard deviation for the 100 calls are 8.2 minutes and 10 minutes, respectively. (a)Do you think the data collected on the 100 seniors are approximately bell-shaped? Explain.Bell-shaped data would range from about standard deviation(s) below the mean to standard deviation(s) above the mean. With a mean of 8.2 minutes and standard deviation of 10, the values in this range are possible phone call lengths, so the data be approximately bell-shaped.(b)Is it valid to conduct a one-sample t-test in this situation? Explain.No. The sample size is large enough, but the data are not bell-shaped.Yes. The data are bell-shaped, so it doesn't matter if the sample size is too small. Yes. The sample size is large enough that it doesn't matter if the data are not bell-shaped.Although the sample size is large, we can tell there are multiple extreme outliers present in the data, so a one-sample t-test may not be valid.No. The sample size is too small, and the data are not bell-shaped.(c)In spite of how you may have answered part (b), carry out a test of the hypotheses of interest in this situation. (Use ? = 0.05.)State the null and alternative hypotheses (in minutes). (Enter != for ≠ as needed.)H0:μ=9.3 Ha: Find the test statistic.___ Use technology to find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.Fail to reject H0. There is sufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Reject H0. There is insufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool. Reject H0. There is sufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Fail to reject H0. There is insufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Use your results to make a recommendation to the cell phone company about whether to offer the senior discount.Based on these results, the company ___ offer the senior discount.

Name: A cell phone company knows that the mean length of calls for all of it
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A cell phone company knows that the mean length of calls for all of its customers in a certain city is 9.3 minutes. The company is thinking about offering a senior discount to attract new customers, but only wants to do so if the mean length of calls

Question

A cell phone company knows that the mean length of calls for all of its customers in a certain city is 9.3 minutes. The company is thinking about offering a senior discount to attract new customers, but only wants to do so if the mean length of calls for current customers who are seniors (65 and over) is lower than it is for the general customer pool. The only way to identify seniors is to conduct a survey and ask people whether they are over age 65. Using this method, the company contacts a random sample of 100 seniors and records the length of their last call. The sample mean and standard deviation for the 100 calls are 8.2 minutes and 10 minutes, respectively. (a)Do you think the data collected on the 100 seniors are approximately bell-shaped? Explain.Bell-shaped data would range from about      standard deviation(s) below the mean to      standard deviation(s) above the mean. With a mean of 8.2 minutes and standard deviation of 10,     the values in this range are possible phone call lengths, so the data     be approximately bell-shaped.(b)Is it valid to conduct a one-sample t-test in this situation? Explain.No. The sample size is large enough, but the data are not bell-shaped.Yes. The data are bell-shaped, so it doesn't matter if the sample size is too small.     Yes. The sample size is large enough that it doesn't matter if the data are not bell-shaped.Although the sample size is large, we can tell there are multiple extreme outliers present in the data, so a one-sample t-test may not be valid.No. The sample size is too small, and the data are not bell-shaped.(c)In spite of how you may have answered part (b), carry out a test of the hypotheses of interest in this situation. (Use ? = 0.05.)State the null and alternative hypotheses (in minutes). (Enter != for ≠ as needed.)H0:μ=9.3 Ha: Find the test statistic.___ Use technology to find the p-value. (Round your answer to four decimal places.)p-value =State your conclusion.Fail to reject H0. There is sufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Reject H0. There is insufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.    Reject H0. There is sufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Fail to reject H0. There is insufficient evidence to conclude the mean phone call length for senior customers is less than the mean length for the general customer pool.Use your results to make a recommendation to the cell phone company about whether to offer the senior discount.Based on these results, the company  ___   offer the senior discount.

Accepted Answer

Given data is appropriate for testing of hypothesis to test z-test for single mean. because the…