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Chapter 8: Q.1.1 (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 the random sample is not satisfied.

Step by step solution

01

Given Information

Number of success (x)=17

Number of trials (n)=100

02

Explanation

The sample was picked based on the school's convenience for children who arrive early, and using the basic random sampling technique is one of the conditions for generating the confidence interval for population percentage. As a result, in this circumstance, the criteria of a simple random sample is not met.

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Most popular questions from this chapter

What inference method will you use? Check that the conditions for using this procedure are met.

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铃�andn1-p铃�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

Hallux abducto valgus (call it HAV) is a deformation of the big toe that is fairly uncommon in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in a random sample of patients under the age of 21who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. For these 21patients, the mean HAV angle was 24.76degrees and the standard deviation was 6.34degrees. A dot plot of the data revealed no outliers or strong skewness.

(a) Construct and interpret a 90%confidence interval for the mean HAV angle in the population of all such patients.

(b) Researchers omitted one patient with an HAV angle of 50degrees from the analysis due to a measurement issue. What effect would including this outlier have on the confidence interval in (a)? Justify your answer.

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.

Starting a nightclub A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that about 70% of the student body would respond favorably. What sample size is required to obtain a 90% con铿乨ence interval with an approximate margin of error of 0.04? Show your work
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