Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Q. T11.6 (page 765)

Which of the following statements about chi-square distributions are true?

I. For all chi-square distributions, P(x2≥0)=1

II. A chi-square distribution with fewer than 10degrees of freedom is roughly symmetric.

III. The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

Short Answer

Expert verified

Option(d) is correct. Statement I and III are correct about chi-square distributions.

Step by step solution

01

Given information

We need to find correct statement about chi-square distributions.

02

Simplify

Statement I-

Because the chi-square distribution is specified solely for non-negative numbers, Statement I is correct.
Hence, P(x2≥0)=1
Statement II-

It is incorrect since the chi-square distribution is always biassed to the right, hence it can't be a nearly symmetric distribution with less than 10 degrees of freedom.
Statement III-

It is correct because the degrees of freedom are the mean of the chi-square distribution.
As a result, as the degrees of freedom increase, the mean rises.

Therefore, Statement I and III are 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 100 students

and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

An appropriate null hypothesis to test whether the food choices are equally popular is

a. H0:μ=25where μ=the mean number of students that prefer each type of food.

b. H0:p=0.25where p = the proportion of all students who prefer ramen.

c. H0:nR=nT=nP=nH=25where nRis the number of students in the school who would choose ramen, and so on.

d.H0:pR=pT=pP=pH=0.25where pRis the proportion of students in the school who would choose ramen, and so on.

e. H0:pR=pT=pP=pH=0.25, where pRis the proportion of students in the sample who chose ramen, and so on.

Preventing strokes Refer to Exercise 38. Which treatment seems to be most effective? Least effective? Justify your choices.

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test H0: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

We compute the value of the χ2test statistic to be 6.57. Assuming that the conditions for inference are met, which of the following is the correct P-value?

a. Greater than0.20

b. Between 0.10and0.20

c. Between 0.05and0.10

d. Between 0.01and0.05

e. Less than0.01

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades 4,5,and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades 4,5,and 6?

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:

The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?

a. Because 0.0129 is less than α=0.05 reject H0 . There is convincing evidence that the food choices are equally popular.

b. Because 0.0129 is less than α=0.05 reject H0 There is not convincing

evidence that the food choices are equally popular.

c. Because 0.0129 is less than α=0.05 reject H0 . There is convincing evidence that the food choices are not equally popular.

d. Because 0.0129 is less than α=0.05 fail to reject H0 There is not convincing evidence that the food choices are equally popular.

e. Because 0.0129 is less than α=0.05 fail to reject H0 There is convincing

evidence that the food choices are equally popular.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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