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Chapter 11: Q 7. (page 716)

No chi-square A school’s 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

Fewer TVs? The United States Energy Information Administration periodically surveys a random sample of U.S. households to determine how they use energy. One of the variables they track is how many TVs are in a household (None, 1,2,3,4,or5or more). The computer output compares the distribution of number of TVs for households in 2009and2015.

Cell Contents: Count

Expected count

Contribution to Chi-square

Chi-Squarerole="math" localid="1654195309908" =137.137, DF =5, P-Value =0.000

a. Which chi-square test is appropriate to analyze these data? Explain your answer.

b. Show how the numbers 252and 14.113were obtained for the 2009/Nonecell.

c. Which 3cells contribute most to the chi-square test statistic? How do the observed and expected counts compare for these cells?

For these data, χ2=69.8with a P-value of approximately 0. Assuming that the researchers used a significance level of 0.05, which of the following is true?

a. A Type I error is possible.

b. A Type II error is possible.

c. Both a Type I and a Type II error are possible.

d. There is no chance of making a Type I or Type II error because the P-value is approximately 0.

e. There is no chance of making a Type I or Type II error because the calculations are correct.

Distance from home A study of first-year college students asked separate random samples of students from private and public universities the following question: “How many miles is this university from your permanent home?” Students had to choose from the following options:5or fewer, 6to 10,11to 50,51to 100,101to 500, or more than 500. Here is the two-way table summarizing the responses:

a. Should we use a chi-square test for homogeneity or a chi-square test for independence in this setting? Justify your answer.

b. State appropriate hypotheses for performing the type of test you chose in part (a). Here is Minitab output from a chi-square test.

c. Check that the conditions for carrying out the test are met.

d. Interpret the P-value. What conclusion would you draw?

Seagulls by the seashore Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200 seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks.

a. Do these data provide convincing evidence that seagulls show a preference for where they land?

b. Relative to the proportion of each ground type on the shore, which type of ground do the seagulls seem to prefer the most? The least?

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:
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