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Chapter 8: Q. 73 (page 520)

In each of the following situations, discuss whether it would be appropriate to construct a one-sample tinterval to estimate the population mean.

(a) We collect data from a random sample of adult residents in a state. Our goal is to estimate the overall percentage of adults in the state who are college graduates.

(b) The coach of a college men鈥檚 basketball team records the resting heart rates of the 15team members. We use these data to construct a confidence interval for the mean resting heart rate of all male students at this college.

(c) Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The Fathom boxplot below displays the difference (texts calls) for each student.

Short Answer

Expert verified

(a) The z-procedure is used when estimating the population proportion. Therefore t- procedure is not used.

(b) We do not use t- procedure.

(c) We do not use t- procedure.

Step by step solution

01

Part(a) Step 1: Given Information

02

Part(a) Step 2: Explanation

The overall percentage of adults is a population proportion.

The t-procedure is used when estimating a population mean and not for the population proportion.

03

Part(b) Step 1: Given Information

04

Part(b) Step 2: Explanation

The sample is a convenience sample because the individuals were conveniently selected as the team members.

A convenience sample is NOT a random sample and thus the RANDOM requirement for the t-procedure is not satisfied.

05

Part(c) Step 1: Given Information

06

Part(c) Step 2: Explanation

In the boxplot we note that there are 3outliers and the distribution appears to be right-skewed (since the line in the box of the boxplot is more to the left of the box).

Since the distribution contains outliers and skewness, the distribution is NOT approximately a normal distribution.

The NORMAL requirement to use the t-procedure is thus not satisfied.

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Most popular questions from this chapter

NAEP scores Refer to Exercise 5. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals?

62. Blink When two lights close together blink alternately, we 鈥渟ee鈥� one light moving back and forth if the time between blinks is short. What is the
longest interval of time between blinks that preserves the illusion of motion? Ask subjects to turn a knob that slows the blinking until they 鈥渟ee鈥� two lights rather than one light moving. A report gives the results in the form 鈥渕ean plus or minus the standard error of the mean.鈥� Data for 12 subjects are summarized as 251卤45 (in milliseconds).
(a) Find the sample standard deviation sx for these measurements. Show your work.
(b) Explain why the interval 251卤45 is not a confidence interval.

In a poll,

I. Some people refused to answer questions.

II. People without telephones could not be in the sample.

III. Some people never answered the phone in several calls.

Which of these sources is included in the 卤2%margin of error announced for the poll?

(a) I only

(b) II only

(c) III only

(d) I, II, and III

(e) None of these

Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019adults. A newspaper article about the poll said, 鈥淩esults have a margin of sampling error of plus or minus 3 percentage points.鈥�15

(a) The news article said that 65% of men, but only 43% of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give con铿乨ence intervals for men and women separately.

(b) Would a 95% con铿乨ence interval for women alone have a margin of error less than 0.03, about equal to 0.03, or greater than 0.03? Why? (You see that the news article鈥檚 statement about the margin of error for poll results is a bit misleading.)

What critical value t鈰�from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of t鈰�. What advantage does the more accurate df provide?
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