1. To conduct a nonparametric test,

A) the population must follow the normal distribution.

B) the standard deviation must be known.

C) it is not necessary to make any assumption about the shape of the population.

D) the data must be at least interval scale.

2. Which of the following is true of the χ² distribution?

A) It is a discrete probability distribution.

B) The χ² statistic is always greater than or equal to zero.

C) It is negatively skewed.

D) It approaches a uniform distribution as the degrees of freedom increase.

3. In a goodness-of-fit test where the sample of 200 observations are distributed among 5 categories, what is the critical value of χ² for a significance level of .05?

A) 9.488

B) 11.070

C) 43.773

D) 195.000

4. A goodness-of-fit test requires that:

A) all the cell frequencies must be the same.

B) there must be at least 30 observations.

C) forty percent of the cells must contain at least 10 observations.

D) expected cell frequencies should be 5 or more.

5. Which statement best describes a contingency table?

A) The table must have equal numbers of rows and columns.

B) The table summarizes one variable that is classified according to two criteria.

C) The table requires at least 10 observations in each cell.

D) The table summarizes the frequencies of two variables.

6. In a contingency table a sample of 400 people is classified by gender and four hair colors (blond, brown, black, and red). How many degrees of freedom are there?

A) 1

B) 3

C) 8

D) 399

7. Which statement is true for a χ² goodness-of-fit test?

A) There is only one degree of freedom.

B) The rejection region is in the upper right tail.

C) The scale of measurement is interval.

D) We must assume a normal population.

8. To find the expected frequency in a contingency table, you must:

A) compute the square root of the degrees of freedom.

B) multiple the row total by the column total and divide the result by the grand total.

C) subtract one from the total number of observations.

D) divide the total number of observations by the number of cells in the table.

9. A researcher collects a random sample of 120 observations to study a demographic variable that is classified into 6 categories. We wish to investigate whether the number of observations is the same in each of the categories for the population. Which test is this?

A) This is a χ² test with 5 degrees of freedom.

B) This is a χ² test with 97 degrees of freedom.

C) This is a χ² test with 3 degrees of freedom.

D) This is a student's t-test with 5 degrees of freedom.

10. Under what conditions could the χ2 distribution assume negative values?

A) When the sample size is small

B) When the cell frequencies are all equal

C) When the degrees of freedom is 1

D) It can never assume negative values

11. In a goodness-of-fit test, the null hypothesis is:

A) H₀: χ² = 0.

B) H₀: Expected frequencies = Observed frequencies.

C) H₀: µ = 0.

D) H₀: The number of classes is equal to the number of observed frequencies.

12. In a contingency table, the null hypothesis is:

A) H₀: χ² = 0.

B) H₀: Expected frequencies = Observed frequencies.

C) H₀: No relationship between two variables.

D) H₀: The number of classes is equal to the number of observed frequencies.

13. For H₀: π = 0.70, α = 0.05, using p = .85 and n = 100, what is the decision regarding the null hypothesis?

A) The null hypothesis is accepted.

B) Fail to reject the null hypothesis.

C) Reject the null hypothesis.

D) Reject the alternative hypothesis.