Chapter 10: Q. 7 (page 665)

At a baseball game, $42$ of $65$ randomly selected people report owning an iPod. At a rock concert occurring at the same time across town, $34$ of $52$ randomly selected people to report owning 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 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) Since the confidence interval includes $0$ , the researcher can conclude that the proportion of iPod owners at the two venues is the same.
(b) Since the confidence interval includes $0$ , the researcher can conclude that the proportion of iPod owners at the two venues is different.
(c) Since the confidence interval includes $0$ , the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
(d) Since 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

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

Step by step solution

Given information

The number of people at baseball owning iPod is $42 o f 65$

The number of people at rock concerts owning iPod is $34 o f 52$

Confidence interval $(- 0.154, 0.138)$

Find the correct outcome of the researcher’s test of the claim.

Explanation

The given confidence interval is

$(- 0.154, 0.138)$

The presence of $0$ in the confidence interval suggests that the population proportions are extremely likely to be equal, therefore we cannot conclude that they are different.