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# Hypothesis testing : Five step method

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10.30. In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At &#945; = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.

10.44. Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study, researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age 58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the inactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret the results at &#945; = .01. (c) Is normality assured? (d) Is the difference large enough to be important? (e) What else would medical researchers need to know before prescribing this drug widely? (Data are from Science News 153 [May 30, 1998], p. 343.)

10.46. To test the hypothesis that students who finish an exam first get better grades, Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with a standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with standard deviation of 24.9. Is this a significant difference at &#945; = .05? (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interpret these results. (c) Is the difference in mean scores large enough to be important? (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at &#945; = .05, showing all steps clearly.

10.58. A ski company in Vail owns two ski shops, one on the west side and one on the east side of Vail. Ski hat sales data (in dollars) for a random sample of 5 Saturdays during the 2004 season showed the following results. Is there a significant difference in sales dollars of hats between the west side and east side stores at the 5 percent level of significance? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the test statistic and state your conclusion. Hats

Saturday Sales Data (\$) for Ski Hats
Statistic East Side Shop West Side Shop
1 548 523
2 493 721
3 609 695
4 567 510
5 432 532

1. Is the mean salary of accountants who have reached partnership status higher than that for accountants who are not partners? A sample of 15 accountants who have the partnerships status showed a mean salary of \$82,000 with a standard deviation of \$5,500. A sample of 12 accountants who were not partners showed a mean of \$78,000 with a standard deviation of \$6,500. At the 0.05 significance level can we conclude that accountants at the partnership level earn larger salaries?

1) State the null and alternate hypothesis
H0:
H1:

2) State the decision rule (What rules, if statement)

3) Compute the value of the test statistic

4) What is your decision regarding the null hypothesis?

5) At the 0.05 significance level can we conclude that accountants at the partnership level earn larger salaries?