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Chapter 11: Q 7. (page 716)

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.

Short Answer

Expert verified

Because the given variable is quantitative, a chi-square test for goodness of fit is not acceptable.

Step by step solution

01

Given information

02

Explanation

Categorical variable: It describes the data's quality or features. It has no numerical or quantitative value.

Quantitative variable: The variable is numerically stated and has a numerical value.

The "average time" variable is a quantitative variable. For categorical variables, we know that the chi-square test is utilized. As a result, doing a chi-square test for goodness on it would be inappropriate.

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Most popular questions from this chapter

Opinions about the death penaltyThe General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor鈥檚 degree, 鈥淒o you favor or oppose the death penalty for persons convicted of murder?鈥� Of the 1379people with only a high school degree, 1010 favored the death penalty, while 319of the 504people with a bachelor鈥檚 degree favored the death penalty. We can test the hypothesis of 鈥渘o difference鈥� in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.

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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

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, 鈥淲hich type of food do you prefer: Ramen, tacos, pizza, or hamburgers?鈥� Here are her data:

The chi-square test statistic is

a. (18鈭�25)225+(22鈭�25)225+(39鈭�25)225+(21鈭�25)225

b. (25鈭�18)218+(25鈭�22)222+(25鈭�39)239+(25鈭�21)221

c. (18鈭�25)25+(22鈭�25)25+(39鈭�25)25+(21鈭�25)25

d. (18鈭�25)2100+(22鈭�25)2100+(39鈭�25)2100+(21鈭�25)2100

e. (0.18鈭�0.25)20.25+(0.22鈭�0.25)20.25+(0.39鈭�0.25)20.25+(0.21鈭�0.25)20.25
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