ATMs must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. But if too much cash is unnecessarily kept in the ATMs, the bank is forgoing the opportunity of investing the money and earning interest. Suppose that at a particular branch the population mean amount of money withdrawn from ATMs per customer transaction over the weekend is $160 with a population standard deviation of $20. If a random sample of 25 customer transactions indicates that the sample mean withdrawal amount is $164, is there evidence to believe that the population mean withdrawal amount is no longer $160? (Use a 0.05 level of significance)

12. State the null and alternative hypothesis. (4 points)

A. Ho: < 160; Ha: 160

B. Ho: 160; Ha: 160

C. Ho: 160; Ha: < 160

D. Ho: = 160; Ha: 160

13. What test should be used to reject the null hypothesis? (4 points)

1. Z test two tail
2. t test two tail
3. Z test one tail
4. t test one tail

14. Assuming the significance level is 0.05, what is the critical value that you should use? (4 points)

A. 1.96

B. 1.64

C. -1.96

D. -1.64

15. What is the computed value of the sample statistic? (4 points)

A. - 1

B. -1.75

C. 1

D. 1.75

16. what are the decision and conclusion of the test at the significance level of 0.05? (4 points)

A. Fail to reject the null hypothesis, there is sufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.

B. Fail to reject the null hypothesis; there is insufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.

C. Reject the null hypothesis; there is sufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.

D. Reject the null hypothesis; there is insufficient evidence to conclude that the mean amount of cash withdrawn per customer from the ATM machine is not equal to $160.

17. what is the p-value? (4 points)

A. 0.10

B. 0.16

C. 0.20

D. 0.32

18. what is the meaning of the p-value? (4 points)

A. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.10 if the population mean is indeed $160.

B. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.16 if the population mean is indeed $160.

C. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.20 if the population mean is indeed $160.

D. The probability of observing a Z test statistic more extreme than the computed sample test statistic is 0.32 if the population mean is indeed $160.

19. What is the conclusion if you use the p-value approach? (4 points)

a. Reject the null

b. Accept the null

20. Do you need any assumption about the population distribution to conduct the test? (4 points)

a. Yes

b. No