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Chapter 11: Q 22. (page 718)

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:

Which of the following is false?

a. A chi-square distribution with k degrees of freedom is more right-skewed than a chi square distribution with k+1 degrees of freedom.

b. A chi-square distribution never takes negative values.

c. The degrees of freedom for a chi-square test are determined by the sample size.

d. P(蠂2>10) is greater when df=k+1 than when df=k

e. The area under a chi-square density curve is always equal to 1

Short Answer

Expert verified

The correct option is (c).

Step by step solution

01

Given information

02

Calculation

Option c is wrong among the possibilities presented. The number of categories determines the degrees of freedom of a chi-square test. df=c-1 is the formula. As a result, sample size has no bearing on degrees of freedom.

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Most popular questions from this chapter

More P-values For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.

a. 蠂2=4.49,df=5

b. 蠂2=4.49,df=1

Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A 3-year study with 72chronic cocaine users compared an antidepressant drug called desipramine with lithium (a standard drug to treat cocaine addiction) and a placebo. One-third of the subjects were randomly assigned to receive each treatment. At the end of the study, researchers recorded whether or not the subjects relapsed. Which of the following conditions must be satisfied to perform the appropriate chi-square test using the data from this study?

I. The population distribution is approximately Normal.

II. The treatments were randomly assigned.

III. The observed counts are all at least 5.

a. I only

b. II only

c. III only

d. II and III

e. I, II, and III

Stress and heart attacks You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:

One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only 3of the 33people in the stress management group suffered "cardiac events," defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, 7of the 34people in the exercise group and 12out of the 40patients in usual care suffered such events.

a. Use the information in the news article to make a two-way table that describes the study results.

b. Compare the success rates of the three treatments in preventing cardiac events.

c. Do the data provide convincing evidence at the 伪=0.05level that the true success rates for patients like these are not the same for the three treatments?

Distance from home A study of first-year college students asked separate random samples of students from private and public universities the following question: 鈥淗ow many miles is this university from your permanent home?鈥� 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?

鈥淲ill changing the rating scale on a survey affect how people answer the question?鈥� To find out, the group took an SRS of 50students from an alphabetical roster of the school鈥檚 just over 1000students. The first 22students chosen were asked to rate the cafeteria food on a scale of 1(terrible) to 5(excellent). The remaining 28students were asked to rate the cafeteria food on a scale of 0(terrible) to 4(excellent). Here are the data:

a. Was this an observational study or an experiment? Justify your answer.

b. Explain why it would not be appropriate to perform a chi-square test in this setting.
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