Exam 14: Chi-Square Applications for Nominal Data

i. If there are only two cells in a goodness-of-fit test, we should expect 5 or more frequencies. ii. 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 Iii) The null hypothesis in the goodness-of-fit test is that there is no difference.

A sample of 100 production workers is obtained. The workers are classified by gender (male, female) and by age (under 20, 20 - 29, 30 - 39 and 40 or over). How many degrees of freedom are there?

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?

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 expected frequency for each candidate?

i. For a goodness-of-fit test, the number of degrees of freedom is determined by k - 2, where k is the number of categories. ii. The sum of the expected frequencies in a goodness-of-fit test need not equal the sum of the observed frequencies. Iii) If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined 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 expected frequency for people who are in favour of the project and have less than 45 feet of property foot-frontage?

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

Two chi-square distributions were plotted on the same chart. One distribution was for 3 degrees of freedom and the other was for 12 degrees of freedom. Which distribution would tend to approach a normal distribution?

i. Nonparametric tests require no assumptions about the shape of the population distribution. 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 chi-square distribution with large degrees of freedom approaches a normal distribution.

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

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

i. The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 2. Ii) If there are extremely large differences between observed and expected frequencies the correct decision is to reject H0. Iii) There are 2 degrees of freedom for a contingency table classifying three levels of income with each gender.

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: Using 0.05 as the significance level, what is the critical value for the test statistic?

i. The claim that "male and female University of Toledo students prefer different parking lots on campus" is an example of a chi-square null hypothesis. Ii) For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total. Iii) For contingency table analysis using the chi-square test, multiplying the number of rows minus 1 by the number of columns minus 1 will give you the degrees of freedom.

In the chi-square test, the null hypothesis (no difference between sets of observed and expected frequencies) is rejected when the:

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: The appropriate test to analyze the relationship between gender and speeding is:

The computed chi-square value is positive because the difference between the observed and expected frequencies is:

Which of the following assumptions is necessary to apply a nonparametric test of hypothesis using 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: The degrees of freedom for the analysis is:

i. chi-square test statistic used in a goodness-of-fit test has k - 2 degrees of freedom. ii. A goodness-of-fit test is a nonparametric test involving a set of observed frequencies and a corresponding set of expected frequencies. iii. 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.