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Chapter 8: Q.1.2 (page 487)

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

Short Answer

Expert verified

No, the condition of normality is not satisfied.

Step by step solution

01

GIven Information

Number of success (x) =3

Number of trials (n)=25

02

Explanation

One of the required conditions to construct the confidence interval for proportion is that np^>10

Here,

25(0.12)=3<10

Thus, the conditional normality is not satisfied here.

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Most popular questions from this chapter

Interpret the confidence level.

A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

II. nis so large that both np⏞andn1-p⏞are at least 10.

III. The population is at least 10times as large as the sample.

(a) I only

(c) III only

(c) I, II, and III

(b) II only

(d) I and II only

Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined “frequent binge drinking” as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers

Check conditions for constructing a confidence interval for the parameter

True or false: The interval from 2.84to 7.55has a 95%chance of containing the actual population standard deviation S. Justify your answer.

Refer to Exercise 12. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non-sampling errors”) could affect the accuracy of the59% estimate?
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