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# Analysis of variation and chi-square test

ANALYSIS OF VARIANCE
#10 The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the 0.05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

Banking Retail Insurance
12 8 10
10 8 8
10 6 6
12 8 8

#14 A stock analyst wants to determine whether there is a difference in the mean rate of return for three types of stock: utility, retail, and banking stocks. The following output is obtained:

Analysis of Variance
Source DF SS MS F P
Factor 2 86.49 43.25 13.09 0.001
Error 13 42.95 3.30
Total 15 129.44
Individual 95% C I s for Mean
Based on Pooled StDev
Level N Mean StDev ----------+------------+-------------+-----
Utility 5 17.4000 1.916 (-------+---------)
Retail 5 11.6200 0.356 (--------+---------)
Banking 6 15.400 2.356 (-------+------)
------------+------------+-------------+-----
Pooled StDev = 1.818 12.0 15.0 18.0
a.) Using the 0.05 level significance, is there a difference in the mean rate of return among the three types of stock?

b.) Suppose the null hypothesis is rejected. Can the analyst conclude there is a difference between the mean rates of return for the utility and the retail stocks? Explain.

NONPARAMETRIC METHODS: CHI -SQUARE APPLICATIONS

#10 The chief of security for the Mall of the Dakota was directed to study the problem of missing goods. He selected a sample of 100 boxes that had been tampered with and ascertained that for 60 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 30 other boxes employees had stolen the goods, and for the remaining 10 boxes he blamed poor inventory control. In his report the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.02 significance level.

See attached file for full problem description.

#### Solution Summary

To test if shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely.

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