A manager was assigned the task of investigating the error in payments for routine purchases made by the purchasing department. The manager randomly selected 12 payments, investigated them thoroughly, and determined the payment error for each of these payments. The payment error was defined as the difference between the amount paid and what should have been paid. The payment errors determined for these selected payments were as follows: $17$25$14-$10$20$40
$35$30$28$22$15$16
(1) Determine the (two-sided) 95% confidence interval for the population mean payment error, and type the value of the upper bound in your (two-sided) confidence interval. (You don’t need to type the value of the lower bound in the confidence interval). Please keep your answer with 2 decimal places.
(2) Suppose a recent company report inferred that the mean payment error may be running as high as $25. That led the manager to use the same data set in Question 39 (and reproduced here for convenience) to test the null hypothesis that the population mean payment error is equal to $25 versus the alternative that the population mean payment error is not equal to $25. Using a level of significance equal to 0.01, perform a (two-sided) t-test. What is the value of the t test statistic? Please type your answer with 2 decimal places.
$17$25$14-$10$20$40
$35$30$28$22$15$16
(3) Suppose another manager used this same data set in Question 39 (reproduced here for convenience) to test the null hypothesis that the population mean payment error is less than or equal to $15 versus the alternative that the population mean payment error is greater than $15. What is the critical value of the t test at a level of significance equal to 0.01? Please type your answer with 3 decimal places.
$17$25$14-$10$20$40
$35$30$28$22$15$16