/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 A school district conducts a sur... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 21

A school district conducts a survey to determine whether voters favor passing a bond to fund school renovation projects. All registered voters are called. Of those called, \(15 \%\) answer the survey call. Of those who respond, \(62 \%\) say they favor passing the bond. Give a reason why the school district should be cautious about predicting that the bond will pass.

Short Answer

Expert verified
The school district should be careful about predicting the bond's passage because only a small proportion (9.3%) of all registered voters have indicated they would vote in favor of the bond. Survey response rates can impact the accuracy of predictions. Non-respondents might have differing opinions, introducing bias into the prediction.

Step by step solution

01

Identify the sample and the population

In this case, the sample are the registered voters who responded to the call, and the population is all registered voters.
02

Calculate the actual percentage of voters in favor

The percentage of registered voters that responded to the call and are in favor of passing the bond needs to be calculated. This can be done by multiplying the percentage of respondents (15%) by the percentage of those in favor (62%). The calculation is \(0.15 \times 0.62 = 0.093\), or \(9.3\%\). This means that only \(9.3\%\) of all registered voters indicated they would vote in favor of the bond.
03

Analyze the bias in survey sampling

The remaining voters who didn't respond to the survey may have different opinions on the bond issue. Hence, the result of the survey might not truly represent the opinion of all registered voters. The survey may introduce a bias known as non-response bias, where respondents may be fundamentally different from non-respondents, which could skew the results.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose it is known that \(60 \%\) of employees at a company use a Flexible Spending Account (FSA) benefit. a. If a random sample of 200 employees is selected, do we expect that exactly \(60 \%\) of the sample uses an FSA? Why or why not? b. Find the standard error for samples of size 200 drawn from this population. What adjustments could be made to the sampling method to produce a sample proportion that is more precise?

A random sample of likely voters showed that \(55 \%\) planned to vote for Candidate \(\mathrm{X}\), with a margin of error of 2 percentage points and with a \(95 \%\) confidence level. a. Use a carefully worded sentence to report the \(95 \%\) confidence interval for the percentage of voters who plan to vote for Candidate \(\mathrm{X}\). b. Is there evidence that Candidate \(\mathrm{X}\) could lose. c. Suppose the survey was taken on the streets of New York City and the candidate was running for U.S. president. Explain how that would affect your conclusion.

a. If a rifleman's gunsight is adjusted incorrectly, he might shoot bullets consistently close to 2 feet left of the bull's-eye target. Draw a sketch of the target with the bullet holes. Does this show lack of precision or bias? b. Draw a second sketch of the target if the shots are both unbiased and precise (have little variation). The rifleman's aim is not perfect, so your sketches should show more than one bullet hole.

A 2017 Gallup poll reported that 658 out of 1028 U.S. adults believe that marijuana should be legalized. When Gallup first polled U.S. adults about this subject in 1969 , only \(12 \%\) supported legalization. Assume the conditions for using the CLT are met. a. Find and interpret a \(99 \%\) confidence interval for the proportion of U.S. adults in 2017 that believe marijuana should be legalized. b. Find and interpret a \(95 \%\) confidence interval for this population parameter. c. Find the margin of error for each of the confidence intervals found in parts a and b. d. Without computing it, how would the margin of error of a \(90 \%\) confidence interval compare with the margin of error for the \(95 \%\) and \(99 \%\) intervals? Construct the \(90 \%\) confidence interval to see if your prediction was correct.

The Perry Preschool Project was created in the early 1960 s by David Weikart in Ypsilanti, Michigan. In this project, 123 African American children were randomly assigned to one of two groups: One group enrolled in the Perry Preschool, and one group did not enroll. Follow-up studies were done for decades. One research question was whether attendance at preschool had an effect on high school graduation. The table shows whether the students graduated from regular high school or not and includes girls only (Schweinhart et al. 2005). $$\begin{array}{lcc}\hline & \text { Preschool } & \text { No Preschool } \\\\\hline \text { HS Grad } & 21 & 8 \\ \text { No HS Grad } & 4 & 17\end{array}$$ a. Find the percentages that graduated for both groups, and compare them descriptively. Does this suggest that preschool was associated with a higher graduation rate? b. Which of the conditions fail so that we cannot use a confidence interval for the difference between proportions?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.