13 questions

30 minutes

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1. An engineer wishes to determine the difference in life expectancies of two brands of batteries. Suppose the standard deviation of each brand is 4.5 hours. How large a sample (same number) of each type of battery should be taken if the engineer wishes to be 90% certain of knowing the difference in life expectancies to within 1 hour?

2. Two confidence interval estimates from the same sample are (16.4, 29.8) and (14.3, 31.9). What is the sample mean, and if one estimate is at the 95% level while the other is at the 99% level, which is which?

3. Two 90% confidence interval estimates are obtained: I (28.5, 34.5) and II (30.3, 38.2).

a. If the sample sizes are the same, which has the larger standard deviation?

b. If the sample standard deviations are the same, which has the larger size?

4. Suppose (25, 30) is a 90% confidence interval estimate for a population mean µ. Which of the following are true statements?

5. Under what conditions would it be meaningful to construct a confidence interval estimate when the data consist of the entire population?

6. A social scientist wishes to determine the difference between the percentage of Los Angeles marriages and the percentage of New York marriages that end in divorce in the first year. How large a sample (same for each group) should be taken to estimate the difference to within ±0.07 at the 94% confidence level?

7. What is the critical t-value for finding a 90% confidence interval estimate from a sample of 15 observations?

8. Acute renal graft rejection can occur years after the graft. In one study (The Lancet, December 24, 1994, page 1737), 21 patients showed such late acute rejection when the ages of their grafts (in years) were 9, 2, 7, 1, 4, 7, 9, 6, 2, 3, 7, 6, 2, 3, 1, 2, 3, 1, 1, 2, and 7, respectively. Establish a 90% confidence interval estimate for the ages of renal grafts that undergo late acute rejection.

9. Nine subjects, 87 to 96 years old, were given 8 weeks of progressive resistance weight training (Journal of the American Medical Association, June 13, 1990, page 3032). Strength before and after training for each individual was measured as maximum weight (in kilograms) lifted by left knee extension:

Find a 95% confidence interval estimate for the strength gain.

10. A catch of five fish of a certain species yielded the following ounces of protein per pound of fish: 3.1, 3.5, 3.2, 2.8, and 3.4. What is a 90% confidence interval estimate for ounces of protein per pound of this species of fish?

11. In a random sample of 25 professional baseball players, their salaries (in millions of dollars) and batting averages result in the following regression analysis:

Which of the following gives a 98% confidence interval for the slope of the regression line?

12. Is there a relationship between mishandled-baggage rates (number of mishandled bags per 1000 passengers) and percentage of on-time arrivals? Regression analysis of ten airlines gives the following TI-Nspire output (baggage rate is independent variable):

13. Smoking is a known risk factor for cardiovascular and cancer diseases. A recent study (Rusanen et al., Archives of Internal Medicine, October 25, 2010) surveyed 21,123 members of a California health care system looking at smoking levels and risk of dementia (as measured by the Cox hazard ratio). Results are summarized in the following graph of 95% confidence intervals.

Which of the following is an appropriate conclusion?