MB 3200 Homework #4 ****************************************************************************** Instructions: Solve all the problems. Each problem carries 10 points. Maximum score possible for this Homework is 80 points. Additional Suggestions/Instructions: 1) No need for typing. You can do your work by hand on paper. 2) If you use a regular A-4/Letter Size (8.5\"x11\") paper to do your Homework on one side, perhaps it will be easier for you to scan. LEAVE ONE-INCH MARGIN ALL AROUND SO THAT NOTHING GOES MISSING WHILE SCANNING. Ensure that in the scanned document the content on all pages is laid out Left to Right and Top to Bottom (whether the page is in Portrait or Landscape mode or in a combination there of). 3) Remember to write down your name on the report and number the pages. 4) Create a single scanned file. DO NOT SUBMIT MULTIPLE FILES. Verify and ensure everything with your report is in order so that when opened the layout is top to bottom. Word or pdf formats are acceptable. If you are using Excel ensure page setup is properly taken care of. 5) Name your report file contains in its name, "Your Full Name" and "Homework Number". 6) Upload your report file on Canvas and verify if everything is fine by opening up the uploaded file. It is your responsibility to ensure your report is uploaded properly. 7) Do not wait until the last minute. The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted. If the report does not appear in Canvas by the deadline, zero points will be recorded for you for that HW. No exceptions are entertained for any reason under any circumstance in this regard. 8) If anyone needs help with scanning, please stop by the Information Commons Help Desk by the second floor Rotunda and seek help. They will explain what you need to do and you will be able to scan your work. Their service is totally free of charge for you. Information Commons is open 9 a.m. - 9 p.m. Monday through Thursday; 9 a.m. - 5 p.m. on Friday; and 8 a.m. - 5 p.m. on Saturday. ****************************************************************************** 1 1) The manager of the Danvers- Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim. a) Which form of the hypotheses should be used to test the manager's claim? Explain. b) What conclusion is appropriate when H0 cannot be rejected? c) What conclusion is appropriate when H0 can be rejected? 2) A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether under-filling or overfilling is occurring. If the sample data lead to a conclusion of under-filling or overfilling, the production line will be shut down and adjusted to obtain proper filling. a) Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line. b) Comment on the conclusion and the decision when H0 cannot be rejected. c) Comment on the conclusion and the decision when H0 can be rejected. 3) CarpetPlace salespersons average $5,000 per week in sales. Steve Jobs, the firm's vice president, proposes a new compensation plan with selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the new compensation plan increases the average sales per salesperson. a) Develop the appropriate null and alternative hypotheses. b) What is the Type I error in this situation? What are the consequences of making this error? c) What is the Type II error in this situation? What are the consequences of making this error? 4) Department of Labor reported the average hourly earnings for production workers to be $15.23 per hour in 2001. A sample of 75 production workers during 2003 showed a sample mean of $15.86 per hour. Assuming the population standard deviation is $1.50, can we conclude that an increase occurred in the mean hourly earnings since 2001? Use = .05. 5) ABC Securities Firm paid out record year-end bonuses of $150,000 per employee for 2005. Suppose we would like to take a sample of employees at the ABC Securities firm to see whether the mean year-end bonus is different from the reported mean of $150,000 for the population. a) State the null and alternative hypotheses you would use to test whether the year-end bonuses paid by ABC Securities were different from the population mean. b) Suppose a sample of 40 employees showed a sample mean year-end bonus of $130,000. Assume a population standard deviation of $30,000 and compute the p- value. c) With a .05 as the level of significance, what is your conclusion? d) Repeat the preceding hypothesis test using the critical value approach. 2 6) Find t values from t distribution tables for the following: a) Area in the upper tail = 0.025 and Sample Size = 101 b) Area in the upper tail = 0.01 and Sample Size = 83 c) Area in the upper tail = 0.05 and Sample Size = 67 d) Area in the lower tail = 0.005 and Sample Size = 18 e) Area in the lower tail = 0.10 and Sample Size = 26 7) Find the chi-square values from chi-square distribution tables. a) 20.005 with Sample Size = 101 b) 20.10 with Sample Size = 30 c) 20.05 with Sample Size = 16 d) 20.995 with Sample Size = 19 e) 20.99 with Sample Size = 96 8) Find the upper critical values based on F distribution tables (given, variance of sample 1 is greater than variance of sample 2). Alpha and Sample Sizes are as follows: a) = .05 with n1 = 6 and n2 = 11 b) = .025 with n1 = 21 and n2 = 26 c) = .01 with n1 = 61 and n2 = 61 d) = .10 with n1 = 9 and n2 = 25 e) = .025 with n1 = 31 and n2 = 23 3