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Chapter 11: Q. 33 (page 754)

Sorry, no chi-square How do U.S. residents who travel overseas for leisure differ from

those who travel for business? The following is the breakdown by occupation.

Occupation
Leisure travelers (%)
Business travelers (%)
Professional/technical
36
39
Manager/executive
23
48
Retired
14
3
Student
7
3
Other
20
7
Total
100
100

Explain why we can’t use a chi-square test to learn whether these two distributions differ

significantly.

Short Answer

Expert verified

We can’t use a chi-square test to learn whether these two distributions differ significantly because the information given to us is in percentage and no information is given about total number of travellers.

Step by step solution

01

Step 1:Given Information 

We have been given that,

Percentage of U.S. residents who travel overseas for leisure,and

Percentage of U.S. residents who travel overseas for business.

Occupation
Leisure travelers (%)
Business travelers (%)
Professional/technical
36
39
Manager/executive
23
48
Retired
14
3
Student
7
3
Other
20
3
Total
100
100
02

Step 2:Explanation 

The information given to us is in percentage and no information is given about total number of travellers.

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Most popular questions from this chapter

Which of the following statements about chi-square distributions are true?

I. For all chi-square distributions, P(x2≥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 100 students

and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

An appropriate null hypothesis to test whether the food choices are equally popular is

a. H0:μ=25where μ=the mean number of students that prefer each type of food.

b. H0:p=0.25where p = the proportion of all students who prefer ramen.

c. H0:nR=nT=nP=nH=25where nRis the number of students in the school who would choose ramen, and so on.

d.H0:pR=pT=pP=pH=0.25where pRis the proportion of students in the school who would choose ramen, and so on.

e. H0:pR=pT=pP=pH=0.25, where pRis the proportion of students in the sample who chose ramen, and so on.

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 α=0.05level that the true success rates for patients like these are not the same for the three treatments?

Birds in the trees Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees are Douglas firs, 40% are ponderosa pines, and 6% are other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees.

a. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they’re searching for seeds and insects?

b. Relative to the proportion of each tree type in the forest, which type of trees do the nuthatches seem to prefer the most? The least?

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.
See all solutions

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