**Q1. If we are testing for the difference between the means of two (2) independent populations with samples n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
**

a. 39.

b. 38.

c. 19.

d. 18.

**Q2. Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test:
**

s12 = 4 and n1 = 16

s22 = 6 and n2 = 25

a. df = 41

b. df = 39

c. df = 16

d. df = 25

**Q3. **A supermarket is interested in finding out whether the mean weekly sales volume of Coca-Cola are the same when the soft drinks are displayed on the top shelf and when they are displayed on the bottom shelf. Ten stores are randomly selected from the supermarket chain with 5 stores using the top shelf display and 5 stores using the bottom shelf display. Assume that the samples are normally distributed with equal population variances. Refer to the sales volume data in the table below, what is the number of degree of freedom?

Top Shelf Sales Volume 23 35 50 68 32

Bottom Shelf Sales Volume 55 70 72 51 63

a. 8

b. 3

c. 10

d. 12

**Q4. **A supermarket is interested in finding out whether the mean weekly sales volume of Coca-Cola are the same when the soft drinks are displayed on the top shelf and when they are displayed on the bottom shelf. Ten stores are randomly selected from the supermarket chain with 5 stores using the top shelf display and 5 stores using the bottom shelf display. Assume that the samples are normally distributed with equal population variances. Refer to the sales volume data in the table below, What are the critical values using a level of significance alpha=.01?

Top Shelf Sales Volume 23 35 50 68 32

Bottom Shelf Sales Volume 55 70 72 51 63

a. +2.7638 and -2.7638

b. +2.8965 and -2.8965

c. +3.3554 and -3.3554

d. +4.5407 and -4.5407

**Q5.** A supermarket is interested in finding out wheather the mean weekly sales volume of Coca-Cola are the same when the softdrinks are displayed on the top shelf and when they are displayed on the bottom shelf. 10 stores are randomly selected from the supermaket chain with 5 stores using the top shelf display and 5 stores using the bottom shelf display. Assume that the samples are normally distributed with equal population variances. Refere to the sales volume data in the table below, Top shelf Sales Mean=41.6, Variance=249.84, Bottom shelf sales Mean=62.2, Variance=66.96.

**What is the sample pooled variance Sp2?
**

Top Shelf Sales Volume 23 35 50 68 32

Bottom Shelf Sales Volume 55 70 72 51 63

a. 158.4

b. 11.995

c. 0

d. -11.995

**Q6.** A supermarket is interested in finding out whether the mean weekly sales volume of Coca-Cola are the same when the soft drinks are displayed on the top shelf and when they are displayed on the bottom shelf. 10 stores are randomly selected from the supermarket chain with 5 stores using the top shelf display and 5 stores using the bottom shelf display. Assume that the samples are normally distributed with equal population variances. Refer to the sales volume data in the table below, Top shelf Sales Mean=41.6, Variance=249.84, Bottom shelf sales Mean=62.2, Variance=66.96.

What is the t-test statistic?

Top Shelf Sales Volume 23 35 50 68 32

Bottom Shelf Sales Volume 55 70 72 51 63

a. -2.588

b. -9.405

c. 9.405

d. 2.13

**Q7. When testing for the difference between the variances of two population with sample sizes of n1= 8 and n2= 10, the number of degrees of freedom is(are): **

a. 8 and 10.

b. 7 and 9.

c. 18.

d. 16.

**Q8. If we are testing for the difference between the means of two (2) related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
**

a. 39.

b. 38.

c. 19.

d. 18.

**Q9. In testing for the differences between the means of two related populations, we assume that the differences follow a _______ distribution.**

a. normal

b. odd

c. sample

d. population

**Q10. The objective of Analysis of Variance (ANOVA) is to analyze differences among the group means.**

a. true

b. false

**Q11. The F test used for testing the difference in two population variances is always a one-tailed test.**

a. true

b. false

**Q12. In testing for the differences between the means of two independent populations, we assume that the 2 populations each follow a _______ distribution.**

a. sample

b. normal

c. odd

d. experiment

**Q13. The statistical distribution used for testing the difference between two population variances is the ___ distribution.**

a. t

b. standardized normal

c. binomial

d. F

**Q14. **One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. A defect rate in terms of High, Average or Low is calculated for each worker in a yearly evaluation. The results for 100 workers based on years of experiences are given in the table below.

Referring to the Table below, at alpha =0.05 level of significance, what would be the decision rule?

<1 Year <1-4 Year <5-9 Year

High 6 9 9

Average 9 19 23

Low 7 8 10

a. Reject H0 if chi-square > 16.919

b. Reject H0 if chi-square > 15.507

c. Reject H0 if chi-square > 11.143

d. Reject H0 if chi-square > 9.488

**Q15. If we use the chi-square method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:**

a. 3

b. 4

c. 5

d. 1

**Q16. The Marascuilo procedures allows one to make comparisons between all pairs of group to figure out which of the population proportions differ.**

a. true

b. false

**Q17. A test for the difference between two proportions can be performed using the chi-square distribution.**

a. true

b. false

**Q18. When testing for independence in a contingency table with 3 rows and 4 columns, there are________ degrees of freedom.**

a. 5

b. 6

c. 7

d. 12

**Q19.** One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. A defect rate in terms of High, Average or Low is calculated for each worker in a yearly evaluation. The results for 100 workers based on years of experiences are given in the table below.

Referring to the Table below, which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

<1 Year <1-4 Year <5-9 Year

High 6 9 9

Average 9 19 23

Low 7 8 10

a. chi-square test for independence

b. chi-square test for differences between two proportions (independent samples)

c. chi-square test for differences between two proportions (related samples)

d. chi-square test for differences among more than two proportions

**Q20.** A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and (2) seat belt usage (worn or not worn) during the accident. Referring to the Table below, at 5% level of significance, the critical value of the test statistic is

Hispanic Non-Hispanic

Seat belts worn 31 148

Seat belts not worn 283 330

a. 3.8415

b. 5.9914

c. 9.4877

d. 13.2767

**Q21. In testing the difference between two proportions using the normal distribution, we may use either a one-tailed Chi-square test or two-tailed Z test.**

a. true

b. false

**Q22. As the number of degrees of freedom increases, the chi-square distribution becomes**

a. progressively more symmetrical

b. progressively more right-skewed

c. progressively more left-skewed

d. The shape is not affected by the degrees of freedom.

**Q23. The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.**

a. true

b. false

**Q24. If we wish to determine whether there is evidence that the proportion of successes is the same in group 1 as in group 2, the appropriate test to use is**

a. the Z test.

b. the chi-square test.

c. Both of the above.

d. None of the above.

**Q25. In testing a hypothesis using the chi-squared test, the expected frequencies are based on the**

a. assumption the null hypothesis is true: the proportion of successes in the two populations are equal.

b. the null hypothesis is false: the proportion of successes in the two populations are not equal.

c. normal distribution.

d. None of the above.