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Chapter 10: Q. 9 (page 666)

How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65and older? To find out, researchers perform a completely randomized experiment involving 1000healthy males in this age group. Half of the subjects are assigned to receive drug treatment only, while the other half are assigned to exercise regularly and to receive drug treatment. The most appropriate inference method for answering the original research question is

(a) one-sample z test for a proportion.

(b) two-sample z interval forp1-p2

(c) two-sample z test for p1-p2.

(d) two-sample t interval for μ1-μ2.

(e) two-sample t-test for μ1-μ2.

Short Answer

Expert verified

The most appropriate inference method for answering the original research question is option (b) two-sample z interval forp1-p2.

Step by step solution

01

Given information

Rate of heart attack among men is 65

Healthy males is 1000

02

Explanation

One proportion: one-sample z test/interval

Two proportions: two-sample z test/interval

One mean: one-sample t-test Two means: two-sample t-test/interval or paired t-test/interval/interval

Use a test if you want to test for a difference, equality, increase or decrease. Use an interval if you want to estimate an interval in which the true value lies.

Two-sample z interval for a proportion differencep1-p2.

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Most popular questions from this chapter

A researcher wants to determine whether or not a five-week crash diet is effective over a long period of time. A random sample of 15 dieters is selected. Each person's weight is recorded before starting the diet and one year after it is concluded. Based on the data shown below (weight in pounds), can we conclude that the diet has a long-term effect, that is, that dieters managed to not regain the weight they lost? Include appropriate statistical evidence to justify your answer.

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine’s manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean 27ounces and standard deviation 0.8ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean 17ounces and standard deviation 0.5ounces. To test the manufacturer’s claim, the restaurant manager measures the amount of liquid in a random sample of 25cups filled with the medium setting and a separate random sample of 20 cups filled with the large setting. Let x1-x¯2be the difference in the sample mean amount of liquid under the two settings (large – medium). Find the probability thatx¯1-x¯2 is more than 12 ounces. Show your work.

National Park rangers keep data on the bears that inhabit their park. Below is a histogram of the weights of 143bears measured in a recent year.

Which statement below is correct?

(a) The median will lie in the interval (140,180), and the mean will lie in the interval (180,220).

(b) The median will lie in the interval (140,180), and the mean will lie in the interval (260,300).

(c) The median will lie in the interval (100,140), and the mean will lie in the interval (180,220).

(d) The mean will lie in the interval (140,180), and the median will lie in the interval (260,300).

(e) The mean will lie in the interval (100,140), and the median will lie in the interval (180,200).

A 96% confidence interval for the proportion of the labor force that is unemployed in a certain city is (0.07,0.10). Which of the following statements about this interval is true?

(a) The probability is 0.96that between 7%and 10%of the labor force is unemployed.

(b) About 96%of the intervals constructed by this method will contain the true proportion of unemployed in the city.

(c) The probability is 0.04that less than 7%or more than 10%of the labor force is unemployed.

(d) The true rate of unemployment lies within this interval 96%of the time.

(e) Between 7%and 10%of the labor force is unemployed96% of the time.

Down the toilet A company that makes hotel toilets claims that its new pressure-assisted toilet reduces the average amount of water used by more than 0.5a gallon per flush when compared to its current model. To test this claim, the company randomly selects 30toilets of each type and measures the amount of water that is used when each toilet is flushed once. For the current-model toilets, the mean amount of water used is1.64a gal with a standard deviation of 0.29gal. For the new toilets, the mean amount of water used is 1.09galwith a standard deviation of 0.18gal.

(a) Carry out an appropriate significance test. What conclusion would you draw? (Note that the null hypothesis is notH0:μ1-μ2=0-

(b) Based on your conclusion in part (a), could you have made a Type I error or a Type Il error? Justify your answer.
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