Description
Please use the excel formulas, thank you:)
Unformatted Attachment Preview
Lightbulb
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Lifetime
840.08
960.00
953.38
981.14
938.66
1051.14
907.84
1000.10
1073.20
1150.66
1010.57
791.59
896.24
955.35
937.94
1113.18
1108.81
773.62
1038.43
1126.55
950.23
1038.19
1136.67
1031.55
1074.28
976.90
1046.30
986.54
1014.83
920.73
1083.41
873.59
902.92
1049.17
998.58
1010.89
1028.71
1049.92
1080.95
1026.41
958.95
985.17
988.49
1012.99
1070.82
1063.13
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948.57
1156.42
973.79
845.85
1025.35
931.60
931.69
1063.00
971.95
689.52
999.63
966.65
1022.77
1041.44
987.74
887.28
975.27
904.52
937.41
964.32
1047.56
1109.78
1053.21
1091.02
1114.46
967.33
1131.02
920.96
983.79
972.49
1001.50
811.08
1035.06
1001.30
970.45
1111.68
955.20
920.79
941.75
937.89
1024.13
952.33
879.74
866.77
1080.00
1002.06
1038.74
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1017.37
988.42
893.74
1022.92
1081.83
1154.07
827.85
Box
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Amount
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174
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376
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363
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360
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QMB 3200
Homework #5
Instructions:
1) Solve all the problems. Each problem carries 10 points. Maximum score possible for this
Homework is 110 points.
2) Presenting only the final answer is not sufficient to get complete credit. Show the steps in solution
approach. That way partial credit can be earned to various steps in final solution. It is your
responsibility to demonstrate mastery of the subject matter through your answers.
3) Submit your report as an Excel file. Solve each problem on a separate tab (worksheet). No
Exceptions. Organize your solutions on the Excel worksheet properly. Show where your answers are for
each problem and the sections of the problem. Use Proper formatting
4) Name Your File to show your Full Name and the HW Number
5) 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.
6) 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 your file does not appear on 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.
HW Problems:
1) The manager of the Danvers- Hilton Resort Hotel stated that the mean guest bill for a week-end 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.
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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 α = .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.
6) Find the data for the problem in the first worksheet named LightbulbLife of the data file QMB3200Homework#5Data.xlsx. It gives the data on the lifetime in hours of a sample of 100 lightbulbs. The
company manufacturing these bulbs wants to know whether it can claim that its lightbulbs typically
last more than 1000 burning hours. So it did a study.
a. Identify the null and the alternate hypotheses for this study.
b. Can this lightbulb manufacturer claim at a significance level of 5% that its lightbulbs typically
last more than 1000 hours? What about at 1%? Test your hypothesis using both, the critical
value approach and the p-value approach. Clearly state your conclusions.
c. Under what situation would a Type-I error occur? What would be the consequences of a
Type-I error?
d. Under what situation would a Type-II error occur? What would be the consequences of a
Type-II error?
7) A manufacturer of raisin bran cereal claims that each box of cereal has more than 200 grams of
raisins. The firm selects a random sample of 64 boxes and records the amount of raisin (in grams) in
each box. The data is provided on the second worksheet named Raisins in the data file QMB3200Homework#5Data.xlsx.
a. Identify the null and the alternate hypotheses for this study.
b. Is there statistical support for the manufacturer’s claim at a significance level of 5%? What
about at 1%? Test your hypothesis using both, the critical value approach and the p-value
approach. Clearly state your conclusions.
c. Under what situation would a Type-I error occur? What would be the consequences of a
Type-I error?
d. Under what situation would a Type-II error occur? What would be the consequences of a
Type-II error?
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8) At Western University the historical mean of scholarship examination score for freshman applications
is 1000. Population standard deviation is known to be 200. Each year, the assistant dean uses a sample
of applications to determine whether the mean examination score for the new freshman applications
has changed. A sample of 100 applications provided a mean of 1050.
a) State the hypotheses to test whether the mean examination score for the new freshman applications has
changed.
b) What is the 95% confidence interval estimate of the population mean examination score?
c) Use the 95% confidence interval to conduct a hypothesis test. What is your conclusion?
d) Assuming α = .05, conduct p-value based hypothesis test. What is the conclusion?
e) Assuming α = .05 conduct a critical-value based hypothesis tests. What is the conclusion?
f) How do the results compare in all the three cases?
9) Refer “Summary on Excel functions for Continuous Probability Distributions and Sampling
Distributions.docx”. Use Excel functions and find the t-values for the following cases.
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
10) Refer “Summary on Excel functions for Continuous Probability Distributions and Sampling
Distributions.docx”. Use Excel functions and find the chi-square values for the following cases. The
area values indicated as the subscript for χ2 are the areas in the upper tail.
a) χ20.005 with Sample Size = 101
b) χ20.10 with Sample Size = 30
c) χ20.05 with Sample Size = 16
d) χ20.995 with Sample Size = 19
e) χ20.99 with Sample Size = 96
11) Refer “Summary on Excel functions for Continuous Probability Distributions and Sampling
Distributions.docx”. Use Excel functions and find the F upper critical values. Alpha (the area in the
upper tail) and Sample Sizes are as follows:
a) α = .05 with n1 = 6 and n2 = 11
b) α = .025 with n1 = 21 and n2 = 26
c) α = .01 with n1 = 61 and n2 = 61
d) α = .10 with n1 = 9 and n2 = 25
e) α = .025 with n1 = 31 and n2 = 23
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