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Chapter 8: Q 9. (page 507)

Shoes The AP Statistics class in Exercise 1 also asked an SRS of 20boys at their school how many pairs of shoes they have. A 95%confidence interval for μG-μB=the true difference in the mean number of pairs of shoes for girls and

boys is 10.9to26.5.

a. Interpret the confidence interval.

b. Does the confidence interval give convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school? Explain your answer.

Short Answer

Expert verified

a. There is 95%confidence interval.

b. The confidence interval gives enough convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school.

Step by step solution

01

Given Information

It is given that for 95%confidence interval, true difference in mean number of shoes for boys and girls are(10.9,26.5)

02

a. Estimating Confidence Interval

From give data, there is 95%assurance that true mean number of pair of shoes of girls is greater than true mean number of pair of shoes for boys.

03

b. To Explain that the confidence interval gives convincing evidence for difference in the true mean number of pairs of shoes for boys and girls at the school

We can observe that confidence interval is containing zero. Hence, it is not likely that there is not any difference in mean number of pair of shoes for boys and girls. Hence, there is convincing evidence for difference in the true mean number of pairs of shoes for boys and girls at the school .

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Most popular questions from this chapter

Most people can roll their tongues, but many can’t. The ability to roll the tongue is

genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400students and find that 317can roll their tongues. The margin of error for a 95%confidence interval for the true proportion of tongue rollers among students is closest to which of the following?

a. 0.0008

b. 0.02

c. 0.03

d. 0.04

e. 0.05

Going to the prom Tonya wants to estimate the proportion of seniors in her school who plan to attend the prom. She interviews an SRS of 20of the 750seniors in her school and finds that 36plan to go to the prom.

More cheating Refer to Exercise 36. Calculate and interpret the standard error of p^for these data.

Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3percentage points to 1.5percentage points. How should they adjust their sample size?

a. Multiply the sample size by 4.

b. Multiply the sample size by 2.

c. Multiply the sample size by 1/2.

d. Multiply the sample size by 1/4.

e. There is not enough information to answer this question.

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution.

a. When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.
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