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Chapter 11: Q.69 (page 658)

Decide whether the following statements are true or false:

As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Given Information

As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical.

02

Explanation

We have to check whether the given statement is true or false:

The chi-squared distribution with k degrees of freedom remains the allocation of a sum of the squares of k independent standard normal random variables.

Therefore, the statement "as the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical" is true.

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Most popular questions from this chapter

Table 11.42contains information from a survey among 499participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the USA. Perform a hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the USA obese population.

Age Class (Years) Obese Expected (percentage) Obese Observed (Frequencies)
20-30
22.4
122
31-40
18.6
104
41-50
12.8
78
51-60
10.4
64
61-70
35.8
168

Table11.42

Read the statement and decide whether it is true or false.

The test to use when determining if the college or university a student chooses to attend is related to his or her socioeconomic status is a test for independence.

What is the test statistic?

The marital status distribution of the U.S. male population, ages 15and older, is as shown in Table 11.35.

Martial Status Percent Frequency
never married 31.3
married 56.1
widowed 2.5
divorced /separated 10.1

The number of births per woman in China is 1.6down from 5.91in 1966. This fertility rate has been attributed to the law passed in 1979restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50women across China the number of births they had had. The results are shown in Table. Does the students鈥� survey indicate that the standard deviation is greater than 0.75?

# of birthsFrequency0513021035
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