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We have presented a contingency table that gives a cross-classification of a random sample of values for two variables x and y, of a population.

Perform the following tasks

a. Find the expected frequencies Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

Short Answer

Expert verified

the data provide sufficient evidence to conclude that the two variables are associated at

the 5% significance level

Step by step solution

01

Step 1. Given

02

Step 2. Solution a). Find the Expected frequencies using MINITAB

MINITAB procedure:

Step 1: Choose Stat > Tables > Chi-Square test for association.

Step 2. In Columns containing the table, enter the column of A, B and C

Step 3. In Rows, select y

Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.

Step 5: Click OK.

03

Step 3. MINITAB output

04

Step 4. Row total, column total and grand total

yABCTotal
a101575100
b02575100
Total1040150200
05

Step 5. Expected Frequencies

yABCTotal
a52075100
b52075100
Total1040150200
06

Step 6. Solution b)

Determine the value of chi-squared statistic

From the MINITAB output, the value of chi-squared statistic is 12.5.

07

Step 7. Solution c) 

Check whether or not the data provide sufficient evidence to conclude that the two variables are associated at the 5% significance level

The hypotheses are given below

Null hypothesis:

H0: The two variables are not associated

Alternative hypothesis:

H1: The two variables are associated

08

Step 8. Conclusion for 5% significance level

From the output, the value of test statistic is 12.5and the p-value is 0.002.

Here, the p-value is lesser than the level of significance

That is,p-value(=0.002)<α(=0.05).

Therefore, the null hypothesis is rejected at 5% level

Thus, the data provide sufficient evidence to conclude that the two variables are associated at

the 5% significance level

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Most popular questions from this chapter

To decide whether two variables of a population are associated, we usually need to resort to inferential methods such as the chi-square independence test. Why?

For a χ2-curve with df=10, determine

a. χ0.052

b.χ0.025

Suppose that you have bivariate data for an entire population.

a. How would you decide whether an association exists between the two variables under consideration?

b. Assuming that you make no calculation mistakes, could your conclusion be in error? Explain your answer.

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is mâ‹…n.

12.71 two and three

Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on the characteristics of incoming college freshmen in The American Freshman. Incoming freshmen characterized their political views as liberal, as moderate, and as conservative, For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views. Freshmen Politics. The Higher Education Research Institute of the University of California, Los Angeles, publishes information on the characteristics of incoming college freshmen in The American Freshman. Incoming freshmen characterized their political views as liberal, as moderate, and as conservative, For this year, a random sample of 500 incoming college freshmen yielded the following frequency distribution for political views.

Political view

Frequency

Liberal

147

Moderate

237

Conservative

116

a. Identify the population and variable under consideration here.

b. At the 55 significance level, do the data provide sufficient evidence to conclude that this year's distribution of political views for incoming college freshmen has changed from the 2000 distribution?

c. Repeat part (b), using a significance level of.

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