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Chapter 10: Q. 7 (page 665)

At a baseball game, 42of 65randomly selected people report owning an iPod. At a rock concert occurring at the same time across town, 34of 52randomly 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鈥檚 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鈥檚 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

01

Given information

The number of people at baseball owning iPod is 42of65

The number of people at rock concerts owning iPod is 34of52

Confidence interval(-0.154,0.138)

Find the correct outcome of the researcher鈥檚 test of the claim.

02

Explanation

The given confidence interval is

(-0.154,0.138)

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

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According to sleep researchers, if you are between the ages of 12and18years old, you need 9hours of sleep to be fully functional. A simple random sample of 28students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9hours, with a standard deviation of 2.1hours.If we are interested in whether students at this high school are getting too little sleep, which of the following represents the appropriate null and alternative hypotheses?

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Min Jae carried out the significance test shown below to answer this question. Unfortunately, he made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1-p2=0

Ha:p1-p2>0

where p1=the proportion of Instructor A's students that passed the state exam and p2=the proportion of Instructor B's students that passed the state exam. Since no significance level was stated, I'll use 蟽=0.05

Plan: If conditions are met, I鈥檒l do a two-sample ztest for comparing two proportions.

Random The data came from two random samples of 50students.

- Normal The counts of successes and failures in the two groups -30,20,22, and 28-are all at least 10.

- Independent There are at least 1000 students who take this driving school's class.

Do: From the data, p^1=2050=0.40and p^2=3050=0.60. So the pooled proportion of successes is

p^C=22+3050+50=0.52

- Test statistic

localid="1650450621864" z=(0.40-0.60)-00.52(0.48)100+0.52(0.48)100=-2.83

- p-value From Table A, localid="1650450641188" P(z鈮�-2.83)=1-0.0023=0.9977.

Conclude: The p-value, 0.9977, is greater than 伪=0.05, so we fail to reject the null hypothesis. There is no convincing evidence that Instructor A's pass rate is higher than Instructor B's.
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