Mini-Case #4: Answer the 12 questions below as indicated (be sure to note the required number of decimal places for each of the three Scenarios). This Mini-Case must be uploaded to CANVAS no later than 12 noon on Wednesday, April 13 (no late submissions will be accepted). This Mini-Case is worth 13 points (1 point for each answer and 1 point for Answer format instructions). Scenario 1: A company is tracking its customer satisfaction scores on a quarterly basis by obtaining a random sample of 40 customers and analyzing the average score of the customer's rating. Suppose in the past the average rating score has been 4.1 (with 5 being the best possible) with a standard deviation of 1.32. Answers What is the probability that the next sample of 40 customers will yield an average score greater than 4.2? (Be sure to use Excel's NORM.DIST function to generate th answer. Show your answer to 4 decimal places.) What is the probability that the next sample of 40 customers will yield an average score less than 4.0? (Be sure to use Excel's NORM.DIST function to generate the answer. Show your answer to 4 decimal places.) Scenario 2: A small medical supply company is concerned about the amount of accounts payable that are more than 45 days outstanding. The finance manager takes a sample of 15 accounts that are more than 45 days outstanding and analyzes the amounts. Use this sample to answer the questions that follow. See "One-sample confidence interval for mean with Excel" (Video, 3 min) posted on Canvas under Week Answers 5 for some guidance. $1,074.32 3 What is the standard error? $1,038.73 $1.247.23 $1,084.79 Using the t-distribution, what is the lower limit for a 95% confidence interval for the $1,209.45 true average (u) amount more than 45 days outstanding? $1,165.20 $1,161.54 in Using the t-distribution, what is the upper limit for a 95% confidence interval for the $1,069.32 true average (u) amount more than 45 days outstanding? $1,311.33 $991.22 Using the t-distribution, what is the upper limit for a 90% confidence interval for the $1,321.37 true average (u) amount more than 45 days outstanding? $1,197.38 $1,167.51 Using the t-distribution, what is the lower limit for a 90% confidence interval for the $1,308.27 true average (u) amount more than 45 days outstanding? $1,421.71 True or False. Increasing the sample size (and assuming the standard deviation [remains the same) will increase the width of the confidence interval. a Suppose the medical supply company has 300 total accounts that are more than 45 days outstanding. What is your point estimate for the total value of the 300 account that are more than 45 days outstanding? Scenario 3: A company that manufactures treadmills has one supplier for its electric motors. The company took a random sample from its current supplier and ran the motors until they failed to see how long they might last. The current supplier claims their motor has an average hours-to-failure of 765 hours. Based on the random sample from the supplier's production, the treadmill company suspects the average time-to- faliure is less than 765 hours? Use the t distribution to set up and conduct a hypothesis test and answer the questions that follow. Current 1358 793 587 608 472 562 879 575 1293 705 623 725 569 424 462 765 Answers 10 What is the value of the test statistic for this hypothesis test? Show your answer to three decimal places. 11 What is the the p-value for a one-tailed test? Show your answer to three decimal places. See Section 9.4 "Using Excel." 12 With an alpha of 0.05 and a one-tailed test, should we reject the null hypothesis that the average hours-to-failure for the suppliers is equal? Yes or No