Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q 13. (page 640)

Ban junk food! A CBS News poll asked 606 randomly selected women and 442

randomly selected men, “Do you think putting a special tax on junk food would encourage more people to lose weight?” 170 of the women and 102 of the men said “Yes.” A 99% confidence interval for the difference (Women – Men) in the true proportion of people in each population who would say “Yes” is −0.020to0.120. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

Short Answer

Expert verified

It provides convincing evidence that two population proportions are equal.

Step by step solution

01

Given Information

It is given that at99%confidence interval, we got(-0.020,0.120).

02

Explanation

The given confidence interval has zero in it. Hence, it is likely that difference in proportion is zero and two population proportions are equal.

So, it is possible that population proportions are equal. Therefore, there is no convincing evidence that two population proportions are not equal.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Children make choices Many new products introduced into the market are

targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice). Here are some of the data:

Researchers want to know if a greater proportion of 6- to 7-year-olds can sort correctly than 4- to5-year-olds.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

The correlation between the heights of fathers and the heights of their grownup sons, both measured in inches, isr=0.52. If fathers’ heights were measured in feet instead, the correlation between heights of fathers and heights of sons would be

a. much smaller than 0.52.

b. slightly smaller than 0.52.

c. unchanged; equal to 0.52.

d. slightly larger than 0.52.

e. much larger than 0.52.

An SRS of size 100is taken from Population A with proportion 0.8of successes. An independent SRS of size 400is taken from Population B with proportion 0.5of successes. The sampling distribution of the difference (A − B) in sample proportions has what mean and standard deviation?

a. mean=0.3; standard deviation =1.3

b. mean=0.3; standard deviation =0.40

c. mean=0.3; standard deviation =0.047

d. mean=0.3; standard deviation =0.0022

e. mean=0.3; standard deviation =0.0002

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6hours with a standard deviation of 3hours. The researcher also obtained an independent SRS of 40high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5hours with a standard deviation of 2hours. Suppose that the researcher decides to carry out a significance test of H0: μsuburban=μcity versus a two-sided alternativ

The P-value for the test is 0.048. A correct conclusion is to

a. fail to reject H0because0.048<α=0.05. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

b. fail to reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

c. fail to reject H0because0.048<α=0.05. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.

d. reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

e. reject H0because 0.048<α=0.05 . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

Researchers want to evaluate the effect of a natural product on reducing blood pressure. They plan to carry out a randomized experiment to compare the mean reduction in blood pressure of a treatment (natural product) group and a placebo group. Then they will use the data to perform a test of H0:μT−μP=0versus Ha:μT−μP>0, where μT= the true mean reduction in blood pressure when taking the natural product and μP = the true mean reduction in blood pressure when taking a placebo for subjects like the ones in the experiment. The researchers would like to detect whether the natural product reduces blood pressure by at least 7points more, on average, than the placebo. If groups of size 50are used in the experiment, a twosample t test using α=0.01will have a power of 80%to detect a 7-point difference in mean blood pressure reduction. If the researchers want to be able to detect a 5-point difference instead, then the power of the test

a. would be less than 80%.

b. would be greater than 80%.

c. would still be 80%.

d. could be either less than or greater than 80%.

e. would vary depending on the standard deviation of the data

See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

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.

Sign-up for free