Exam 14: Chi-Square Applications for Nominal Data

i. 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. Ii) 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. Iii) The sum of the expected frequencies and the sum of the observed frequencies must be equal.

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 ? = 0.05?

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.

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.

A school is trying to determine if there is a relationship between gender and which of its 3 programs that students enroll in. 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. What is the chi square value?

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 F's?

The chi-square has:

i. 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. Ii) The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1. Iii) If there are extremely large differences between observed and expected frequencies the correct decision is to accept H0.

Canadian Accounting classifies accounts receivable as "current", "late", and "not collectible". Industry figures show that 60% of A/R are current, 30% are late, and 10% are uncollectible. A law firm in Markham Ontario has 500 accounts receivable: 320 are current, 120 are late and 60 are not collectible. Are these numbers in agreement with the industry distribution?

In a chi-square goodness-of-fit-test, the larger the difference between the set of expected frequencies and the set of observed frequencies:

i. The shape of the chi-square distribution changes for each number of degrees of freedom. ii. The minimum computed value of chi-square is zero. Iii) The chi-square distribution is a positively skewed distribution.

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

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 statistic for the analysis is:

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: How many degrees of freedom are there?

To find the expected frequency in a contingency table:

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.

i. The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test. Ii) The number of degrees of freedom appropriate for the chi-square goodness-of-fit test is the number of categories minus 1. Iii) If there are extremely large differences between observed and expected frequencies the correct decision is to reject H0.

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: What is the value of the test statistic?

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 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?