Exam 14: Chi-Square Applications

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. What is the calculated value of chi-square?

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 5% level of significance? What is your decision at the 1% level of significance?

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.

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

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 kind of frequencies are the numbers 12, 9, 11, 10, and 9 called?

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 null hypothesis for the analysis is:

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. What is the expected number of C's?

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 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 expected frequency for people who are undecided about the project and have property front-footage between 45 and 120 feet?

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. What is your decision if $\alpha$ = 0.05?

i. The chi-square distribution with large degrees of freedom approaches a normal distribution. ii. The chi-square distribution is positively skewed. iii. Nonparametric tests of hypotheses, which are also called distribution free tests, require the population to be normally distributed.

If an employee wanted to investigate the relationship between performance rating and gender, what type of analysis should be used?

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?

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?

A school is trying to determine if there is a relationship between gender and which of its 3 programs that students enroll. It was observed that 20 females enrolled in accounting, 15 in finance and 25 in marketing. For males, 10 enrolled in accounting, 20 enrolled in finance and 15 enrolled in marketing. Can we conclude that there is a relationship between gender and program? Use the 0.05 significance level.

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.

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.

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

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

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. If there are only two cells in a goodness-of-fit test, we should expect 5 or more frequencies. iii. 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.