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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

Exercises 53 and 54 refer to the following setting. The table below displays the number of accidents at a factory during each hour of a 24-hour shift (1  1 a.m).

53. Accidents happen (1.2, 3.1)
(a) Construct a plot that displays the distribution of the number of accidents effectively.
(b) Construct a plot that shows the relationship between the number of accidents and the time when they occurred.
(c) Describe something that the plot in part (a) tells you about the data that the plot in part (b) does not.
(d) Describe something that the plot in part (b) tells you about the data that the plot in part (a) does not.

School vouchers A national opinion poll found that 44% of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.

(a) How large an SRS is required to obtain a margin of error of 0.03(that is, 卤3%) in a 99% con铿乨ence interval? Answer this question using the previous poll鈥檚 result as the guessed value for p鈭�.

(b) Answer the question in part (a) again, but this time use the conservative guess p鈭�=0.5. By how much do the two sample sizes differ?

I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

(c) Increase the sample size.

(d) Use the same confidence level, but compute the interval n times. Approximately5% of these intervals will be larger.

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.

How common is SAT coaching? A random sample of students who took the SAT college entrance examination twice found that 427of the respondents had paid for coaching courses and that the remaining 2733 had not. 1+ Construct and interpret a 99% confidence interval for the proportion of coaching among students who retake the SAT. Follow the four-step process.

64. Vitamin C content Several years ago, the U.S. Agency for International Development provided 238,300 metric tons of corn-soy blend (CSB) for
emergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food. As part of a study to evaluate appropriate vitamin C levels in this food, measurements were taken on samples of CSB produced in a factory. The following data are the amounts of vitamin C,

measured in milligrams per 100grams (mg/100 g) of blend, for a random sample of size8 from one production run:
2631232211221431
Construct and interpret a95%confidence interval for the mean amount of vitamin C M in the CSB from this production run.

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