Exam 14: Chi-Square Applications

The personnel manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are: What is the expected frequency?

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below. If the computed chi-square is 8.5, what is your decision at the 10% level of significance?

The educational level and the social activity of a sample of executives follow. What does the expected frequency for the "above average" social activity and "high school" education equal?

Six people have declared their intentions to run for a trustee seat in the next local election. A political poll is conducted during the campaign among 1,020 voters to determine if there is any clear preference among the voters. The responses are shown below. What is the critical value at the 5% level of significance?

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below. What is the computed value of chi-square?

i. The sum of the expected frequencies and the sum of the observed frequencies must be equal. ii. If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined level of significance. iii. If there are only two cells in a goodness-of-fit test, we should expect 5 or more frequencies.

i. Tests of hypotheses for nominal or ordinal levels of measurement are called nonparametric or distribution-free tests. ii. There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on. iii. The shape of the chi-square distribution depends on the size of the sample.

The following table shows the adjustment to civilian life and place of residence. Using the data from this Mega stat printout, you determine:

For a chi-square test involving a contingency table, suppose the null hypothesis is rejected. We conclude that the two variables are:

i. A goodness-of-fit test is a nonparametric test involving a set of observed frequencies and a corresponding set of expected frequencies. ii. For a goodness-of-fit test, the following are possible null and alternate hypotheses: Null: Sales are uniformly distributed among the five locations. Alternate: Sales are not uniformly distributed among the five locations. iii. In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed set of observations "fits" an "expected" set of observations.

Six people have declared their intentions to run for a trustee seat in the next local election. A political poll is conducted during the campaign among 1,020 voters to determine if there is any clear preference among the voters. The responses are shown below. What is the critical value at the 1% level of significance?

Recently, students in a marketing research class were interested in the driving behavior of students. Specifically, the marketing students were interested if exceeding the speed limit was related to gender. They collected the following responses from 100 randomly selected students: The degrees of freedom for the analysis is:

At a recent car show, a sample of 125 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred.

i. If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined level of significance. ii. The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test. iii. There are 2 degrees of freedom for a contingency table classifying three levels of income with each gender.

A survey of the opinions of property owners about a street widening project was taken to determine whether the resulting opinion was related to the distance of front footage. A randomly selected sample of 100 property owners was contacted and the results are shown below. What kind of table is this classification? Determine the null and alternate hypotheses.

At a recent car show, a sample of 125 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred.

i. The chi-square goodness-of-fit test is appropriate for nominal and ordinal levels of data. ii. Chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom. iii. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies.

The chi-square distribution is:

Suppose that we wish to test the null hypothesis that for 3 cells, A, B, and C, the cell categories are equal. We observed 8 data in cell A, 13 in cell B, and 9 in cell C. What is the decision regarding the null hypothesis?

At a recent automobile show, a sample of 135 people produced the following results. Use the 0.01 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?