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Chapter 11: Q. T 11.2 (page 765)

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25%tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50freshmen, 50sophomores, 50juniors, and 50seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. Here are the results:

The conditions for carrying out the chi-square test in Exercise T11.1 are:

I. Independent random samples from the populations of interest.

II. All sample sizes are less than 10%of the populations of interest.

III. All expected counts are at least 5.

Which of the conditions is (are) satisfied in this case?

a. I only

b. II only

c. I and III only

d. II and III only

e. I, II, and III

Short Answer

Expert verified

The correct option is (e) i.e. I,II and III.

Step by step solution

01

Given information

We need to find the correct option for the given data.

02

Explanation

We know that

Random, independent (10%), and large counts are the parameters for performing a chi-square test of homogeneity/independence.

I. Random: I'm satisfied because the samples are all random.

II. Self-sufficient: Content since the 50pupils from each year represent less than 10%of all students (assuming that the university has at least 500students in each year).

III. High counts: I'm happy because all of the projected counts are at least 5.

As a result, all of the conditions are met, and (e) I, II, and III are right.

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Most popular questions from this chapter

It’s hard for smokers to quit. Perhaps prescribing a drug to fight

depression will work as well as the usual nicotine patch. Perhaps combining the patch and

the drug will work better than either treatment alone. Here are data from a randomized,

double-blind trial that compared four treatments.

A “success” means that the subject did not smoke for a year following the start of the study.

a. Summarize these data in a two-way table.

b. Do the data provide convincing evidence of a difference in the effectiveness of the four

treatments at theα=0.05significance level?

Skittles® Statistics teacher Jason Mole sky contacted Mars, Inc., to ask about the color distribution for Skittles candies. Here is an excerpt from the response he received: “The original flavor blend for the Skittles Bite Size Candies is lemon, green apple, orange, strawberry and grape. They were chosen as a result of consumer preference tests we conducted. The flavor blend is 20 percent of each flavor.”

a. State appropriate hypotheses for a significance test of the company’s claim.

b. Find the expected counts for a random sample of 60 candies.

c. How large a χ2test statistic would you need to have significant evidence against the company’s claim at the α=0.05 level? At the α=0.01 level?

d. Create a set of observed counts for a random sample of 60 candies that gives a P-value between 0.01 and 0.05 Show the calculation of your chi-square test statistic.

Python eggs How is the hatching of water python eggs influenced by the temperature of

the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water

temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the

mother python, and cold duplicates the absence of the mother. Here are segmented bar graphs showing the results of the experiment. Describe what you see.

The two-way table shows the results of the experiment described in

Exercise 28.

Hatching Statuswater temperature:coldwater temperature:neutral
water temperature:hot
Total
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No11
18
29
58
Total
27
56
104
187

a. State the appropriate null and alternative hypotheses.

b. Show the calculation for the expected count in the Cold/Yes cell. Then provide a

complete table of expected counts.

c. Calculate the value of the chi-square test statistic.

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

See all solutions

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