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Chapter 11: Q. 35 (page 725)

How do U.S. residents who travel overseas for leisure differ from those who travel for business? The following is the breakdown by occupation:

Explain why we can鈥檛 use a chi-square test to learn whether these two distributions differ significantly.

Short Answer

Expert verified

We can鈥檛 use a chi-square test to learn whether these two distributions differ significantly because proportions are known instead of actual counts.

Step by step solution

01

Given information

The given data is

02

Explanation

To use the chi-square test, we need to know the actual counts. However, in the table, we note that only the proportions have been given and thus we cannot apply the chi-square test.

Proportions are known instead of actual counts.

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Most popular questions from this chapter

Refer to Exercise 27. Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work

From exercise27

An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is

(a) H0:渭=25, where 渭=the mean number of trees in each quadrant.

(b) H0:p=0.25, where p=the proportion of all trees in the forest that are in Quadrant 1.

(c) H0:n1=n2=n3=n4=25, where niis the number of trees from the sample in Quadrant i.

(d) H0:p1=p2=p3=p4=0.25, where piis the actual proportion of trees in the forest that are in Quadrant i.

(e) H0:p^1=p^2=p^3=p^4=0.25, where p^iis the proportion of trees in the sample that are in Quadranti.

Sorry, no chi-square We would prefer to learn from teachers who know their subject. Perhaps even pre-school children are affected by how knowledgeable they think teachers are. Assign 48three- and four-year-olds at random to be taught the name of a new toy by either an adult who claims to know about the toy or an adult who claims not to know about it. Then ask the children to pick out a picture of the new toy in a set of pictures of other toys and say its name. The response variable is the count of right answers in four tries. Here are the data:

The researchers report that children taught by the teacher who claimed to be knowledgeable did significantly better 蠂2=20.24,P<0.05. Explain why this result isn't valid.

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) 99.

Gregor Mendel (1822鈥�1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or wrinkled. Mendel predicted a ratio of 3smooth peas for every 1 wrinkled pea. In one experiment, he observed 423 smooth and133 wrinkled peas. The data were produced in such a way that the Random and Independent conditions are met. Carry out a chi-square goodness-of-fit test based on Mendel鈥檚 prediction. What do you conclude?
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