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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

Short Answer

Expert verified

(a) H0There is no difference between the distribution of sports goals for females and the distribution of sports goals for males.

Ha: There is a difference between the distribution of sports goals for females and the distribution of sports goals for males.

(b)

(c) The value of the chi-square statistic is 24.8978.

Step by step solution

01

Part (a) Step 1: Given information

The data is

02

Part (a) Step 2: Explanation

The null hypothesis states that there is no association between the variables:

H0: There is no difference between the distribution of sports goals for females and the distribution of sports goals for males.

The alternative hypothesis states that there is an association between the variables:

Ha: There is a difference between the distribution of sports goals for females and the distribution of sports goals for males.

03

Part (b) Step 1: Given information

The data given is

04

Part (b) Step 2: Explanation

From the given

n1=67

n2=67

localid="1650643199717" n=67+67=134

The expected count is the row total multiplied by the sample size divided by the total sample size n=134

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

Observed counts

Expected counts

The chi-square statistic is the sum of squared deviations (between observed and expected counts) divided by the expected count:

2=(14-22.5)222.5+(7-12.5)212.5+(21-13)213+(25-19)219+(3122.5)222.5+(1812.5)212.5+(513)213+(1319)21924.8978

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Most popular questions from this chapter

Refer to Exercises 2 and 4.

(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?

(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.

(c) Use Table C to find the P-value. Then use your calculator鈥檚 C2cdf command.

(d) What conclusion would you draw about whether the roulette wheel is operating correctly? Justify your answer

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(a) Check that the conditions for performing the chi-square test are met.

(b) Use Table C to find the P-value. Then use your calculator鈥檚 C2cdf command.

(c) Interpret the P-value from the calculator in context.

(d) What conclusion would you draw? Justify your answer.

Average ratings (1.3,10.2)The students decided to compare the average ratings of the cafeteria food on the two scales.

(a) Find the mean and standard deviation of the ratings for the students who were given the 1-to-5scale.

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(c) Would it be appropriate to compare the means from parts (a) and (b) using a two-sample t-test? Justify your answer

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Group Treatment Subjects Successes

1 Nicotine patch 244 40

2 Drug 244 74

3 Patch plus drug 245 87

4 Placebo 160 25

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

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

Do the data provide convincing evidence of a difference in the effectiveness of the four treatments? Carry out an appropriate test at the =0.05significance level.

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