10 questions

23 minutes

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1. A judge chosen at random reaches a just decision roughly 80% of the time. What is the probability that in randomly chosen cases at least two out of three judges reach a just decision?

2. Miles per gallon versus speed (miles per hour) for a new model automobile is fitted with a least squares regression line. Following is computer output of the statistical analysis of the data.

Which of the following gives a 99% confidence interval for the slope of the regression line?

3. What fault do all these sampling designs have in common?

I.The Parent-Teacher Association (PTA), concerned about rising teenage pregnancy rates at a high school, randomly picks a sample of high school students and interviews them concerning unprotected sex they have engaged in during the past year.

II.A radio talk show host asks people to phone in their views on whether the United States should keep troops in Bosnia indefinitely to enforce the cease-fire.

III.The Ladies Home Journal plans to predict the winner of a national election based on a survey of its readers.

4. Hospital administrators wish to determine the average length of stay for all surgical patients. A statistician determines that for a 95% confidence level estimate of the average length of stay to within ±0.50 days, 100 surgical patients' records would have to be examined. How many records should be looked at for a 95% confidence level estimate to within ±0.25 days?

5. A chess master wins 80% of her games, loses 5%, and draws the rest. If she receives 1 point for a win, point for a draw, and no points for a loss, what is true about the sampling distribution X of the points scored in two independent games?

6. Which of the following is a true statement?

7. An assembly line machine is supposed to turn out ball bearings with a diameter of 1.25 centimeters. Each morning the first 30 bearings produced are pulled and measured. If their mean diameter is under 1.23 centimeters or over 1.27 centimeters, the machinery is stopped and an engineer is called to make adjustments before production is resumed. The quality control procedure may be viewed as a hypothesis test with the null hypothesis H0: μ = 1.25 and the alternative hypothesis Ha: μ ≠ 1.25. The engineer is asked to make adjustments when the null hypothesis is rejected. In test terminology, what would a Type II error result in?

8. Both over-the-counter niacin and the prescription drug Lipitor are known to lower blood cholesterol levels. In one double-blind study Lipitor outperformed niacin. The 95% confidence interval estimate of the difference in mean cholesterol level lowering was (18, 41). Which of the following is a reasonable conclusion?

9. The following parallel boxplots show the average daily hours of bright sunshine in Liberia, West Africa:

For how many months is the median below 4 hours?

10. Following is a cumulative probability graph for the number of births per day in a city hospital.

Assuming that a birthing room can be used by only one woman per day, how many rooms must the hospital have available to be able to meet the demand at least 90 percent of the days?