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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鈮�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鈮�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.

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Most popular questions from this chapter

Which test?Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.

a. Does chocolate help heart-attack victims live longer? Researchers in Sweden randomly selected 1169people who had suffered heart attacks and asked them about their consumption of chocolate in the previous year. Then the researchers followed these people and recorded whether or not they had died within 8years.

b. Random-digit-dialing telephone surveys used to exclude cell-phone numbers. If the opinions of people who have only cell phones differ from those of people who have landline service, the poll results may not represent the entire adult population. The Pew Research Center interviewed separate random samples of cell-only and landline telephone users who were less than 30years old and asked them to describe their political party affiliation

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a. State appropriate hypotheses for performing a chi-square test for independence in this setting.

b. Compute the expected counts assuming that H0is true.

c. Calculate the chi-square test statistic, df, and P-value.

d. What conclusion would you draw?

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 蠂2test 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

No chi-square A school鈥檚 principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night.

Explain carefully why it would not be appropriate to perform a chi-square test for goodness of fit using these data.

Finger length Is your index finger longer than your ring finger? Or is it the other way around? It isn't the same for everyone. To investigate if there is a relationship between gender and relative finger length, we selected a random sample of 460U.S. high school students who completed a survey. The two-way table shows the results.


Do these data provide convincing evidence at the 伪=0.10level of an association between gender and relative finger length in the population of students who completed the survey?
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