Exam 14: Chi-Square Applications

i. The chi-square distribution is positively skewed. ii. Nonparametric tests of hypothesis, which are also called distribution free tests, require the population to be normally distributed. iii. The computed value of chi-square is always positive because the difference between the observed frequencies and the expected frequencies are squared.

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.

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

To analyze data cross-classified in a contingency table, how are the degrees of freedom found?

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?

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

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. How many degrees of freedom are there?

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. Determine the null and alternate hypotheses.

i. Nonparametric tests require no assumptions about the shape of the population distribution. ii. Tests of hypotheses for nominal or ordinal levels of measurement are called nonparametric or distribution-free tests. iii. 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.

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 grades above B?

i. 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. ii. The null hypothesis in the goodness-of-fit test is that there is no difference. iii. The alternative hypothesis states that there is a difference between the observed frequencies and the expected frequencies in a goodness-of-fit test.

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.

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.

The following table classifies an individual in two ways-by gender and by educational choice. What is this two-way classification 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: Using the output from Mega stat for the data given, what can you conclude?

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.

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. If the computed chi-square is 30, what is your decision at the 1% level of significance? What is your decision at the 5% level of significance?

If we wanted to see if tossing a die (a cube with the sides numbered one through six) had an equal chance of showing each side or number, what statistical test should be applied?

i. Nonparametric tests of hypotheses, which are also called distribution free tests, require the population to be normally distributed. ii. The computed value of chi-square is always positive because the difference between the observed frequencies and the expected frequencies are squared. iii. The shape of the chi-square distribution changes for each number of degrees of freedom.

Which of the following are correct statements regarding the chi-square distribution?