Exam 14: Chi-Square Applications

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?

At a recent car show, a sample of 125 people produced the following results. Calculate the value of chi-square to determine if there is a relationship between age and model preferred.

i. The sum of the expected frequencies in a goodness-of-fit test need not equal the sum of the observed frequencies. 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. Chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom. ii. The chi-square goodness-of-fit test can be applied if there are equal or unequal expected frequencies. iii. For a goodness-of-fit test, the number of degrees of freedom is determined by k - 2, where k is the number of categories.

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

To find the expected frequency in a contingency table:

Which of the following can be used to test if two nominal variables or characteristics are related?

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. A goodness-of-fit test is a nonparametric test involving a set of observed frequencies and a corresponding set of expected frequencies.

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: Based on the analysis, what can be concluded?

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?

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?

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?

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 critical value of chi-square at the 0.05 level?

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?

The chi-square distribution becomes more symmetrical as:

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. 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.

When determining how well an observed set of frequencies fit an expected set of frequencies the test is the:

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 appropriate test statistic for the analysis is:

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? Using the data from this Mega stat printout, you determine: