# Significance Level: Time Spent at Desktop

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 .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

10 10 10

11. Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1 Treatment 2 Treatment 3

8 3 3

11 2 4

10 1 5

3 4

2

1. State the null hypothesis and the alternate hypothesis.

2. What is the decision rule?

3. Compute SST, SSE, and SS total.

4. Complete an ANOVA table.

5. State your decision regarding the null hypothesis.

6. If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.

10

The chief of security for the Mall of the Dakotas 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 to 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 .02 significance level.

19

In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

1. When two samples are selected __________________ of each other, the selection of one sample has no effect on the selection of the other.

2. In order to take advantage of the implications proposed by the ____________________ Theorem, it is desirable to have the size of the samples from two populations both exceed 30.

3. _________________ variables are often used to identify two populations for comparison, even when only a single sample has already been selected.

4. If you know the value of the standard deviation for each of the two populations that you are comparing, the __________________ test statistic applies.

5. Both the null and the alternative hypothesis contain statements about the ____________________ being compared, not the samples.

6. If two population means are not equal to each other, then the difference between them must be some number other than ___________.

7. If the null hypotheses H0: m1 = m2 is true, the difference between the two sample means should be small compared to the size of the _______________________.

8. If it is desired to determine whether the difference between two populations is d, where d ¹ 0, the correct statement of the null hypothesis is ________________.

9. A large-sample test for the difference between two population means requires that _____________ sample sizes be greater than _____________.

10. Finding the rejection region for a hypothesis test involving the Z distribution depends entirely on the value of _____________ and whether the test is _____________-sided or _____________- sided.

11. When the population standard deviations are unknown and the sample sizes are not large, it is necessary to use a ____________ test to compare population means.

12. Instead of using two different estimates of an unknown but common population variance, it makes more sense to combine the data and derive a better estimate of the common variance, the ____________ variance.

13. It is inadvisable to pool the data in order to test for differences between population means whenever the two population variances are _____________.

14. Unlike the standard normal distribution, the number of _______________ directly influences the shape of the t distribution.

15. When sample data are collected before and after an experiment is performed, it is commonly known as _____________ and ______________ data.

16. One of the problems associated with using tests for independent populations is that if there is a large amount of variation among the sample elements, the _________________ of the estimates will be high.

17. If a paired difference test is conducted in which 15 observations are made on the pretest and 15 observations are made on the post-test, the test statistic has a t distribution with ___________ degrees of freedom.

18. Population mean is to quantitative data as population _________________ is to qualitative data.

19. Sample proportions can range in value between __________ and __________, and sample percentages can range in value between ___________ and __________, inclusive.

20. If two numbers are estimates of the same unknown population parameter, their differences will be at or near _____________ and their ratio will be at or near _____________.

21. The F statistic represents a ____________ of two sample variances.

22. The lower critical value of the F statistic is the ________________ of the upper critical value of the F statistic with the degrees of freedom reversed.

23. The F distribution is not symmetric; instead it is ________________.

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#### Solution Summary

The solution provides many fill in the blank answers with explanations of how to properly use a hypothesis test and t-test as well as ANOVA and sample proportions.

Significance Level: Time Spent at Desktop and Other Scenarios

1. 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 .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

10 10 10

2. Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

(see chart in attached file)

a. State the null hypothesis and the alternate hypothesis.

b. What is the decision rule?

c. Compute SST, SSE, and SS total.

d. Complete an ANOVA table.

e. State your decision regarding the null hypothesis.

f. If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.

3. The chief of security for the Mall of the Dakotas 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 to 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 .02 significance level.

4. In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning's local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

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