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Chapter 12: Q.AP4.6 - Cumulative AP Practise Test (page 827)

The town council wants to estimate the proportion of all adults in their medium-sized town who favor a tax increase to support the local school system. Which of the

following sampling plans is most appropriate for estimating this proportion?

a. A random sample of 250names from the local phone book

b. A random sample of 200parents whose children attend one of the local schools

c. A sample consisting of 500people from the city who take an online survey about the issue

d. A random sample of 300homeowners in the town

e. A random sample of 100people from an alphabetical list of all adults who live in the town

Short Answer

Expert verified

The most appropriate sampling plan is

e. A random sample of 100people from an alphabetical list of all adults who live in the town

Step by step solution

01

Given information 

Given in the question that, the town council wants to estimate the proportion of all adults in their medium-sized town who favor a tax increase to support the local school system. We need to find a most appropriate sampling plans for estimating this proportion from the options.

02

Explanation

The town council wants to know how many adults in their medium-sized town support raising taxes to fund the local education system. As a result, we must consider the three conditions for computing a population proportion hypothesis test: random, independent, and normal.

As a result, option (e) is the most appropriate sample plan since everyone in the population is expected to be listed in the alphabetical list of all adults, and because we choose a random sample from the list, the random requirement will be satisfied. The prerequisites are not met in the rest of the options. As a result, option (e) is the proper choice.

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Most popular questions from this chapter

SAT Math scores Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis that used data from all 50states in a recent year. Explain why the conditions for performing inference about the slope β1 of the population regression line are not met.

A study of road rage asked random samples of 596men and 523women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0-20. The respondents were chosen by random-digit dialing of telephone numbers. Are the conditions for inference about a difference in means satisfied?

a. Maybe; the data came from independent random samples, but we should examine the data to check for Normality.

b. No; road rage scores on a scale of 0-20can’t be Normal.

c. No; a paired t-test should be used in this case.

d. Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

e. Yes; we have two independent random samples and large sample sizes, and the10% condition is met.

The school board in a certain school district obtained a random sample of 200residents and asked if they were in favor of raising property taxes to fund the hiring of more statistics teachers. The resulting confidence interval for the true proportion of residents in favor of raising taxes was (0.183,0.257). Which of the following is the margin of error for this confidence interval?

a. 0.037

b. 0.074

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d. 0.220

e.0.257

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Do beavers benefit beetles? Researchers laid out 23circular plots, each 4meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth so beetles prefer them. If so, more stumps should produce more beetle larvae

Here is computer output for regression analysis of these data. Construct and interpret a99% confidence interval for the slope of the population regression line. Assume that the conditions for performing inference are met.

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