Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5%significance level, whether an association exists between the specified pair of variables.

type of community and response

Short Answer

Expert verified

There is no association exists between type of community and response at the 5% significance level.

Step by step solution

01

Step 1. Given  information

Given significance level=5%

The given specified pair of variables.= type of community and response

02

Step 2. Check whether there is an association exists between the specified pair of variables or not. 

The hypotheses are given below:
Null hypothesis:
H0 : There is no association exists between type of community and response.
Alternative hypothesis:
H1 : There is an association exists between type of community and response.

03

Step 3. Use MINITAB to obtain the test statistic and p-value.

MINITAB procedure:
Step 1: Choose Stat > Tables>Chi-Square test for association.
Step 2: In Columns containing the table, enter the column of Male and Female.
Step 3: In Rows, select Response.
Step 4: Under Statistics, select Chi-square test, Display counts in each cell, Display marginal counts and expected cell counts.
Step 5: Click OK.

04

Step 4. Finding MINITAB output

Chi-Square Test for Association: RESPONSE, Worksheet columns

From the MINITAB output,the value of the chi-square statistic is6.952 and the p-value is0.138

05

Step 5. Finding the conclusion for above problem

Here, theP-value is greater than the level of significance.
That is, P-value =0.138)>α(=0.05.
Therefore, the null hypothesis is not rejected at5%level.
Thus, there is no association exists between type of community and response at the 5% significance level.

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Most popular questions from this chapter

For a χ2-curve with df=4, determine

a. χ0.0052

b.χ0.012

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution: 0.2, 0.4, 0.3, 0.1

Observed frequencies: 85, 215, 130, 70

Significance level = 0.05

In each of the given Exercises, 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. For each exercise, 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.

In this exercise, you are to consider two variables, xand ydefined on a hypothetical population. Following are the conditional distributions of the variable ycorresponding to each value of the variablex.
a. Are the variables xandy associated? Explain your answer.
b. Determine the marginal distribution ofy.
c. Can you determine the marginal distribution of x? Explain your answer.

Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.

a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.

b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal

c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?

d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.

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