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Chapter 10: Q. T10.7 (page 698)

At a baseball game, 42of 65randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34of 52randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90%confidence interval for the difference (Game − Concert) in population proportions is (−0.154,0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

a. Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.

b. Because the center of the interval is -0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

c. Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

d. Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

e. The researcher cannot draw a conclusion about a claim without performing a significance test.

Short Answer

Expert verified

Option (c) Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different. is the correct outcome of the researcher’s test of the claim.

Step by step solution

01

Given information

We need to find correct outcome of the researcher’s test of the claim.

02

Simplify

The confidence interval is as follows:

(−0.154,0.138)

Now, we see that the confidence interval contains zero, which suggests that the population proportions are very likely to be equal, and thus we cannot determine that they are different.
As a result, option (c) is the proper choice; the researcher cannot conclude that the fraction of iPod owners at the two venues is different because the confidence interval comprises zero.

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Most popular questions from this chapter

Literacy A researcher reports that 80%of high school graduates, but only 40%of high school dropouts, would pass a basic literacy test. Assume that the researcher’s claim is true. Suppose we give a basic literacy test to a random sample of 60high school graduates and a separate random sample of 75high school dropouts.p^G,p^Dbe the sample proportions of graduates and dropouts, respectively, who pass the test.

a. What is the shape of the sampling distribution of p^G-p^D. Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Does drying barley seeds in a kiln increase the yield of barley? A famous

experiment by William S. Gosset (who discovered the t distributions) investigated this

question. Eleven pairs of adjacent plots were marked out in a large field. For each pair,

regular barley seeds were planted in one plot and kiln-dried seeds were planted in the

other. A coin flip was used to determine which plot in each pair got the regular barley seed

and which got the kiln-dried seed. The following table displays the data on barley yield

(pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05 level

that drying barley seeds in a kiln increases the yield of barley, on average?

Children make choices Refer to Exercise 15.

a. Explain why the sample results give some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

School A has 400students and School B has 2700students. A local newspaper wants to compare the distributions of SAT scores for the two schools. Which of the following would be the most useful for making this comparison?

a. Back-to-back stem plots for A and B

b. A scatterplot of A versus B

c. Two dot plots for A and B drawn on the same scale

d. Two relative frequency histograms of A and B drawn on the same scale

e. Two bar graphs for A and B drawn on the same scale

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of H0:μT−μP=0versus Ha:μT−μP>0, where μT= the true mean reduction in blood pressure when taking the natural product and μP = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least 7points more, on average, than the placebo. If groups of size 50are used in the experiment, a twosample t test using α=0.01will have a power of 80%to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test

a. would be less than 80%.

b. would be greater than 80%.

c. would still be 80%.

d. could be either less than or greater than 80%.

e. would vary depending on the standard deviation of the data

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