1. The χ² statistic from a contingency table with 6 rows and five columns will have:

a. 30 degrees of freedom

b. 24 degrees of freedom

c. 29 degrees of freedom

d. 20 degrees of freedom

e. 25 degrees of freedom

2. The chi-square goodness of fit is _________ a one-tailed test with the rejection region in the right tail.

a. Always

b. Sometimes

c. Never

3. Which if any of the following statements about the chi-square test of independence is false?

a. If r_i is row total for row i and c_j is the column total for column j, then the estimated expected cell frequency corresponding to row i and column j equals (r_i) (c_j)/n

b. The test is valid if all of the estimated cell frequencies are at least five

c. The chi-square statistic is based on (r-1)(c-1) degrees of freedom where r a nd c denote, respectively the number of rows and columns n the contingency table

d. The alternative hypothesis states that the two classifications are statistically independent

e. All of the above statements are true about the chi-square test of independence

4. When we carry out a chi-square test of independence, as the difference between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable:

a. Decreases

b. Increases

c. May decrease or increase depending on the number of rows and columns

d. Will be unaffected

5. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The production supervisor obtained the following data: The Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used. What is the rejection point condition?

a. Reject H₀ if χ²>.10257

b. Reject H₀ if χ²>9.3484

c. Reject H₀ if χ²>5.99147

d. Reject H₀ if χ²>7.37776

e. Reject H₀ if χ²>7.81473

6. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The production supervisor obtained the following data: The Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used. Calculate the expected number of defective units produced by Process 1.

a. 29

b. 21

c. 30

d. 16

e. 15

7. A manufacturing company produces part 2205 for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part 2205 is the same for all three processes. The production supervisor obtained the following data: The Process 1 had 29 defective units in 240 items; Process 2 produced 12 defective units in 180 items and Process 3 manufactured 9 defective units in 150 items. At a significance level of .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used. Calculate the expected number of conforming units produced by Process 2.

a. 15

b. 168

c. 180

d. 164

e. 83