Exam 14: Chi-Square Applications for Nominal Data

At a recent automobile show, a sample of 135 people produced the following results. Use the 0.05 significance level to determine if there is a relationship between age and model preferred. Based on the analysis above, what can be concluded?

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. If the computed chi-square is 30, what is your decision at the 1% level of significance? What is your decision at the 5% level of significance?

How many degrees of freedom do we use for the chi square goodness of fit test?

Three new colors have been proposed for the Jeep Grand Cherokee vehicle. They are silvered-blue, almond, and willow green. The null hypothesis for a goodness-of-fit test would be

What is our decision for a goodness-of-fit test with a computed value of chi-square of 1.273 and a critical value of 13.388?

A student asked a statistics professor if grades were marked "on the curve." The professor decided to give the student a project to determine if last year's statistics grades were normally distributed. The professor told the student that last year's mean mark was 70 with a standard deviation of 10 and to use the following results. Using the data from this Megastat printout, you determine:

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?

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?

Recently, students in a marketing research class were interested in the driving behaviour 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: Based on the analysis, what can be concluded?

What is our decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079?

The educational level and the social activity of a sample of executives follow. Using the data from this Megastat printout, you determine:

The following table classifies an individual in two ways-by gender and by educational choice. Using the data from this Megastat printout, you determine:

i. Chi-square goodness-of-fit test is the appropriate statistical test to use when you wish to determine how well an observed set of data fits an expected set of data Ii) The null hypothesis in the goodness-of-fit test is that there is no difference. Iii) The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test.

i. 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. Ii) The sum of the expected frequencies and the sum of the observed frequencies must be equal. Iii) If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined level of significance.

What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?

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. How many degrees of freedom are there?

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 rule using the 0.05 significance level?

Which of the following are correct statements regarding the chi-square distribution?

i. Nonparametric tests of hypotheses, which are also called distribution free tests, require the population to be normally distributed. Ii) The shape of the chi-square distribution changes for each number of degrees of freedom. iii. The chi-square distribution is a positively skewed distribution.

i. The computed value of chi-square is always positive because the difference between the observed frequencies and the expected frequencies are squared. ii. The shape of the chi-square distribution changes for each number of degrees of freedom. iii. The minimum computed value of chi-square is zero.