Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Q. 55 (page 758)

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877teens (grades 7to 12). One question asked, “What do you think are the chances you will be married in the next 10years?” Here is a two-way table of the responses by gender:

Which of the following is the appropriate null hypothesis for performing a chi-square test?

a. Equal proportions of female and male teenagers are almost certain they will be married in 10years.

b. There is no difference between the distributions of female and male teenagers’ opinions about marriage in this sample.

c. There is no difference between the distributions of female and male teenagers’ opinions about marriage in the population.

d. There is no association between gender and opinion about marriage in the sample.

e. There is no association between gender and opinion about marriage in the population.

Short Answer

Expert verified
Option (e)Ho: There is no correlation between gender and population opinion on marriage.
Ha: In the population, there is a link between gender and attitudes toward marriage.

Step by step solution

01

Given information

We have to determine the state the null and alternative hypotheses.

02

Simplification

The null and alternative hypotheses:

  H0: There is no correlation between gender and population opinion on marriage.

  Ha: In the population, there is a link between gender and attitudes toward marriage.

Hence, option e is correct.

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

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100students and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

Which of the following is false?

a. A chi-square distribution with k degrees of freedom is more right-skewed than a chi square distribution with k+1 degrees of freedom.

b. A chi-square distribution never takes negative values.

c. The degrees of freedom for a chi-square test are determined by the sample size.

d. P(χ2>10) is greater when df=k+1 than when df=k

e. The area under a chi-square density curve is always equal to 1

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25%tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50freshmen, 50sophomores, 50juniors, and 50seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. Here are the results:

Which null hypothesis would be appropriate for performing a chi-square test?

a. The closer students get to graduation, the less likely they are to be opposed to tuition increases.

b. The mean number of students who are strongly opposed is the same for each of the 4years.

c. The distribution of student opinion about the proposed tuition increase is the same for each of the 4years at this university.

d. Year in school and student opinion about the tuition increase are independent in the sample.

e. There is an association between year in school and opinion about the tuition increase at this university.

No chi-square The principal in Exercise 7 also asked the random sample of students to record whether they did all of the homework that was assigned on each of the five school days that week. Here are the data:

The National Longitudinal Study of Adolescent Health interviewed a random sample of 4877teens (grades 7to 12). One question asked, “What do you think are the chances you will be married in the next 10years?” Here is a two-way table of the responses by gender:

Which of the following is the expected count of females who respond “Almost certain”?

a.487.7

b.525

c. 965

d.1038.8

e.1174

Is your random number generator working? Use your calculator’s RandInt function to generate 200 digits from 0 to 9 and store them in a list.

a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator’s random number generator gives each digit an equal chance of being generated.

b. Carry out a test at the α=0.05 significance level. Hint: To obtain the observed

counts, make a histogram of the list containing the 200 random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from −0.5to9.5 with an increment of 1

c. Assuming that a student’s calculator is working properly, what is the probability that the student will make a Type I error in part (b)?

d. Suppose that 25 students in an AP® Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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