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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

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?

93% confidence Find z*fora93%confidence interval using Table A or your calculator. Show your method.

How much does the fat content of Brand Xhot dogs vary? To find out, researchers measured the fat content (in grams) of a random sample of 10Brand X hot dogs. A 95%confidence interval for the population standard deviation Sis 2.84to 7.55.

1. Interpret the confidence interval.

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.

One reason for using a tdistribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

(a) zcan be used only for large samples.

(b) zrequires that you know the population standard deviation 蟽.

(c) zrequires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a zcritical value will lead to a wider interval than a tcritical value.
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