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Chapter 11: Q.4 (page 692)

Roulette Calculate the chi-square statistic for the data in Exercise 2. Show your work.

Short Answer

Expert verified

From the given information, the test statistics are4.0389

Step by step solution

01

Given Information

It is given in the question that,

02

Explanation

Here,

p1=1838=0.4737

p2=1838=0.4737

p3=238=0.0526

The null and alternative hypotheses are:

H0:p1

H0:p2

H0:p3

Hα : At least one of pi is different

The calculation for test statistics is done as:

03

Step 3: Explanation

The test statistic is

χ2=∑(O−E)2/E=4.0389

Therefore, the test statistic is 4.0389

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Most popular questions from this chapter

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 the data on the number of eggs and the number that hatched

(a) Make a two-way table of temperature by outcome (hatched or not). Calculate the proportion of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief?

(b) Are the differences between the three groups statistically significant? Give appropriate evidence to support your answer

Perform a follow-up analysis of the test in Exercise 39 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result?

Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would be more effective for patients who had already had a stroke. Here are the data on strokes during the two years of the study:

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

(b) Make a graph to compare the rates of strokes for the four treatments. Describe what you see.

(c) Explain in words what the null hypothesis H0: p1 = p2 = p3 = p4 says about the incidence of strokes.

(d) Find the expected counts if H0 is true, and display them in a two-way table similar to the table of observed counts

The conditions for carrying out the chi-square test in exercise T11.2 are

I. Separate random samples from the populations of interest.

II. Expected counts large enough.

III. The samples themselves and the individual observations in each sample are independent.

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

(a) I only

(d) Il and III only

(b) II only

(e) I, II, and III

(c) I and II only

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
See all solutions

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