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Use the excel formulas please.
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Homework #6
Instructions:
1) Solve all the problems. Each problem carries 20 points. Maximum score possible for
this Homework is 140 points. When both p-value and critical-value approaches are
asked, you have to use both as points are allocated to various sections and questions
posed in a problem.
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. You must submit
only a single Excel file. Name Your File to show your Full Name and the HW Number.
4) 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.
5) 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. Data from the U.S. Shopper Database provided the following percentages for women
shopping at each of the various outlets. The other category included outlets such as Target,
Kmart, and Sears as well as numerous smaller specialty outlets. No individual outlet in this
group accounted for more than 5% of the women shoppers.
Outlet
Percentage
Other
35
Wal-Mart
25
Department Stores
10
Mail Order
15
Kohl’s
10
J.C. Penney
5
A recent survey using a sample of 200 women shoppers in Tampa, FL found 60 Wal-Mart,
29 traditional department store, 11 JC Penney, 14 Kohl’s, 30 mail order, and 56 other outlet
shoppers. Does this sample suggest that women shoppers in Tampa differ from the
preferences expressed in the U.S. Shopper Data-base? What is your conclusion based on both
the p-value and critical-value approaches? Use α = .01.
1
2. The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 largest
U.S. companies. The performance of each company is rated based on the annual total return,
including stock price changes and the re-investment of dividends. Ratings are assigned by
dividing all 1000 largest U.S. companies into four groups of equal size Group A (top rating),
B (second best rating), C (third best rating), and D (bottom most rating). Shown here are the
one- year ratings for a sample of 50 largest U.S. companies. Does the sample data provide
evidence that the ratings are equally likely for the largest U.S. companies based on both the
p-value and critical-value approaches? Use α = .025.
A
B
C
D
22
9
14
5
3. With double- digit annual percentage increases in the cost of health insurance, more and
more workers are likely to lack health insurance coverage. The following sample data
provide a comparison of workers with and without health insurance coverage for small,
medium, and large companies. For the purposes of this study, small companies are
companies that have fewer than 100 employees. Medium companies have 100 to 999
employees, and large companies have 1000 or more employees. Sample data is reported as
follows:
Health Insurance
Size of Company
Yes
No
Total
Small
Medium
Large
50
25
75
80
20
100
115
10
125
Total
245
55
300
a. Conduct a test of independence using critical-value approach to determine whether
employee health insurance coverage is independent of the size of the company. State
the Hypotheses and the conclusion. Use α = .005.
b. What is the p-value? What is your conclusion based on p-value approach?
c. The USA Today article indicated employees of small companies are more likely to
lack health insurance coverage. Use percentages based on the preceding data to
support this conclusion.
4. FlightStats, Inc., collects data on the number of flights scheduled and the number of flights
flown at major airports throughout the United States. FlightStats data showed 56% of flights
scheduled at Newark, La Guardia, and Kennedy airports were flown during a three-day
snowstorm. All airlines say they always operate within set safety parameters— if conditions
are too poor, they don’t fly. The following data show a sample of 600 scheduled flights
during the snowstorm. Use the chi- square test with a .10 level of significance to determine
whether or not flying/ not flying in a snowstorm is independent of Airliner. State the
Hypotheses. What is your conclusion based on Critical-Value test? Is it any different from
conclusion based on a p-value approach? Sample data follows:
2
Flight
Yes
No
American
70
80
Continental
105
55
Delta
95
85
United
45
65
5. The number of incoming phone calls defined by a Random Variable X at a company
switchboard during 1- minute intervals is believed to have a Poisson distribution. Use a .05
level of significance and the following data to test the assumption that the incoming phone
calls follow a Poisson distribution. State the Hypotheses as well as the conclusion.
x
0
1
2
3
4
5
6
7
8
Observed Freq.
14
33
48
44
30
15
9
6
1
6. A salesperson makes four calls per day. A sample of 100 days gives the following
frequencies of sales volumes.
Number
of Sales
0
1
2
3
4
Observed
Frequency
(Days)
30
40
20
8
2
Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the
number of sales per day should follow a binomial distribution. Assume that the population
has a binomial distribution with n = 4, p =.25, and x = 0, 1, 2, 3, and 4.
a. Compute the expected frequencies for x = 0, 1, 2, 3, and 4 by using the binomial
probability function. Combine categories if necessary to satisfy the requirement that
the expected frequency is five or more for all categories.
b. Use the goodness of fit test to determine whether the assumption of a binomial
distribution should be rejected. State the Hypotheses and the conclusion. Use α = .10.
Note: Because no parameters of the binomial distribution were estimated from the
sample data, the degrees of freedom are k-1 where k is the number of categories.
3
7. A lending institution supplied the following data on loan approvals by four loan officers.
Conduct an appropriate Hypothesis test to determine whether the loan approval decision is
independent of the loan officer reviewing the loan application.
Loan Officer
Sean
Bruce
Debbie
Susie
Total
Loan Approval Decision
Rejected
Approved
14
12
14
18
16
34
16
26
60
90
Total
26
32
50
42
150
a) State the Null and Alternate Hypotheses.
b) Determine the value of the test statistic. Show all the steps in your solution.
c) Determine p-value. Conduct Hypothesis test using p-value approach with α = .025. What
is the test decision?
d) Determine Critical-Value. Conduct Hypothesis test using Critical-Value approach with α
= .05. What is the test decision?
e) Do the results in parts c) and d) lead to different conclusions? Why or Why not?
f) Based on test decisions under parts c) and d), what conclusion would you draw?
4
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