Exam 14: Chi-Square Applications for Nominal Data

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 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. Which of the following statements are correct?

The chi-square distribution becomes more symmetrical as:

Which of the following are correct statements regarding the goodness-of-fit test?

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?

i. The null hypothesis in the goodness-of-fit test is that there is no difference 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) The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1.

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.

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.

The chi-square distribution is:

A school is trying to determine if there is a relationship between gender and which of its 3 programs that students enrol. 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.

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 against the project and who have over 120 feet of property foot-frontage?

i. Small differences between observed and expected frequencies are due to chance. ii. The chi-square distribution with large degrees of freedom approaches a normal distribution. iii. The chi-square distribution is positively skewed.

i. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies. Ii) For a goodness-of-fit test, the number of degrees of freedom is determined by k - 2, where k is the number of categories Iii) The sum of the expected frequencies in a goodness-of-fit test need not equal the sum of the observed frequencies.

i. The chi-square goodness-of-fit test can be applied if there are equal or unequal 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) The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1.

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 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?

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?

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 alternative hypothesis?

A distributor of personal computers has five locations in the city. The sales in units for the first quarter of the year were as follows: What is the critical value at the 0.01 level of risk?

i. For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total. Ii) 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. 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.