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Day Afternoon 10 11 12 14 9 At the .05 significance level, is there a difference in the mean number of defects per shift? (a) State the null hypothesis and the alternate hypothesis. (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding the null hypothesis? (e) What is the p-value? (f ) Interpret the result. (g) What are the assumptions necessary for this test? For Exercises 7 and 8: (a) state the decision rule, (b) compute the pooled estimate of the popula- EXERCISES tion variance, (c) compute the test statistic, (d) state your decision about the null hypothesis, and (e) estimate the p-value. 7. The null and alternate hypotheses are: Ho: My = M 2 A random sample of 10 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4. A random sample of 8 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5. At the .05 significance level, is there a difference between the population means? 8. The null and alternate hypotheses are: Hi My = 1 2 A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the . 10 significance level, is there a difference in the population means?null hypothesis. 13. The null and alternate hypotheses are: Ho: My = 1 2 A random sample of 15 items from the first population showed a mean of 50 and a stan- dard deviation of 5. A sample of 12 items for the second population showed a mean of 46 and a standard deviation of 15. 14. The null and alternate hypotheses are: Ho: My = 12 H : My 7 12 A random sample of 20 items from the first population showed a mean of 100 and a stan- dard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significant level. 15. A recent survey compared the costs of adoption through public and private agencies. For a sample of 16 adoptions through a public agency, the mean cost was $21,045, with a standard deviation of $835. For a sample of 18 adoptions through a private agency, the mean cost was $22,840, with a standard deviation of $1,545. Can we conclude the mean cost is larger for adopting children through a private agency? Use the .05 signifi- cance level. 16. Suppose you are an expert on the fashion industry and wish to gather information to com- pare the amount earned per month by models featuring Liz Claiborne attire with those lease visit of Calvin Klein. The following is the amount ($000) earned per month by a sample of /lind16e 15 Claiborne models: $5.0 $4.5 $3.4 $3.4 $6.0 $3.3 4.8 $4.5 $4.6 $3.5 $5.2 4.4 4.6 3.6 5.0 The following is the amount ($000) earned by a sample of 12 Klein models