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1-What is a Type I error? Explain how the cumulative Type I error affects your decision making. How are the two independent sample t-tests different from ANOVA?
2-Why is the F distribution important? How do you determine if a significant difference exists among the groups in ANOVA? How do you determine differences between the groups in ANOVA?
Describe the requirements that must be met before an ANOVA test may be used. Discuss what the researcher must do if one of these requirements is not met.
10.30 In 1999, a sample of 200 in-store shoppers showed that 42 paid by debit card. In 2004, a sample of the same size showed that 62 paid by debit card. (a) Formulate appropriate hypotheses to test whether the percentage of debit card shoppers increased. (b) Carry out the test at a = .01. (c) Find the p-value. (d) Test whether normality may be assumed.
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 a = .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 a standard deviation of 24.9. Is this a significant difference at a = .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 a = .05, showing all steps clearly.
11.24 In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Crash Damage $
|
Goliath |
Varmint |
Weasel |
||||
|
1600 |
1290 |
1090 |
||||
|
760 |
1400 |
2100 |
||||
|
880 |
1390 |
1830 |
||||
| 1 |
950 |
1850 |
1250 |
|||
|
1220 |
950 |
1920 |
11.24 In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash Damage $
