Question-1: The manager of a department store is thinking about establishing a new billing system for the store's customers. After a thorough financial analysis, she determines that the new system will be cost-effective only if the mean monthly account balance is greater than $250. A random sample of 111 monthly accounts is drawn. The sample mean is $272.50, and the sample standard deviation is $130.00 a) Identify the Null and Alternative hypotheses for a hypothesis test that would allow the manager to decide whether there is sufficient evidence to conclude that the new system will be cost-effective. Using a value of a = .05, identify the critical value(s) of the test statistic used for this hypothesis test. State your conclusion. b) Using the t-table show how you can approximate the p-value of your test. in (a). c) Calculate the 95% confidence interval for the population mean. Briefly explain the meaning of the confidence interval. Based on this confidence interval redo your test in (a). d) Find the smallest value for X that allows you to reject the null in (a). e) (Lecture-3) Find the power of your test in (a) for an alternative of 275. Comment on your answer. (Note: the sample size is large, approximatet with Z) Question-1: The manager of a department store is thinking about establishing a new billing system for the store's customers. After a thorough financial analysis, she determines that the new system will be cost-effective only if the mean monthly account balance is greater than $250. A random sample of 111 monthly accounts is drawn. The sample mean is $272.50, and the sample standard deviation is $130.00 a) Identify the Null and Alternative hypotheses for a hypothesis test that would allow the manager to decide whether there is sufficient evidence to conclude that the new system will be cost-effective. Using a value of a = .05, identify the critical value(s) of the test statistic used for this hypothesis test. State your conclusion. b) Using the t-table show how you can approximate the p-value of your test. in (a). c) Calculate the 95% confidence interval for the population mean. Briefly explain the meaning of the confidence interval. Based on this confidence interval redo your test in (a). d) Find the smallest value for X that allows you to reject the null in (a). e) (Lecture-3) Find the power of your test in (a) for an alternative of 275. Comment on your answer. (Note: the sample size is large, approximatet with Z)