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# How does a t test differ from a z test in terms of when it is used, how it is calculated, and how we determine significance?

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1. A researcher is interested in whether students who attend private elementary schools do any better on s standard test of intelligence than the general population of elementary school children. A random sample of 75 students at a private elementary school is tested and has a mean intelligence test score of 103.5. The average for the general population of elementary school children is 100 (σ = 15).

a) Is this a one- or a two- tailed tests?

#### How many pages is this assigment?

b) What are Ho and Ha for this study?

c) Compute zobt

d) What is zcv?

e) Should Ho be rejected? What should the researcher conclude?

f) Calculate the 95% confidence interval for the population mean, based on the sample mean.

2. Assume that the average person in America weights 150 pounds (μ). You want to determine whether colleges students weigh less than the average America, Following are the wights collected on a sample of colleges students: 120, 105, 166, 170, 145, 149, 135, 115, 168, 138.

a) Is this a one- or two-tailed test?

b) What are Ho and Ha for this study?

c) Compute tobt

d) What is tcv?

e) Should Ho be rejected? What should the researcher conclude?

3. How does a t test differ from a z test in terms of when it is used, how it is calculated, and how we determine significance?

4. According to the U.S. Bureau of the Census, 75% of adults regularly drank alcohol in 1985. An investigator predicts that fewer adults drink now than drank then. A sample of 100 adults is asked about their current drinking habits; 67 report drinking, and 33 report not drinking.

a) What is X2obt?

b) What is (are) the df for this test?

c) What is X2cv?

d) What conclusion should be drawn from these results?

5. A health magazine recently reported a study in which researchers claimed that iron supplements increased memory and problem-solving abilities in a random sample of college women. All of the women took memory and problem-solving tests at the beginning of the study, then took iron supplements, and then took the same tests again at the end of the study. What is wrong with this design? What confounds could be leading to the results of improved memory and problem-solving skills?

6. In an experimental study of the effects of exercise on stress, participants are randomly assigned to either the no exercise or the exercise conditions. Identify what type of study this is—between-, within-, or matched-participants. In addition, identify the independent and dependent variables and the control and experimental groups.

7. What are the advantages and disadvantages in the use of a posttest-only control group design versus a pretest-posttest control group design?

8. What is a confound and how is it related to interval validity?

9. What is the relationship between external validity and the college sophomore problem?

10. Explain what counterbalancing is, how it is achieved, and which confound it helps to minimize.

11. Explain what a Latin square is and how it helps with counterbalancing.

12. According to some research, males have better spatial skills than do females; and according to other research, females have better reading skills than males. A student is interested in determining which sex performs better on a word-search puzzle (a puzzle in which the words are hidden vertically, horizontally, and diagonally within an array of letters) since this type of puzzle involves both spatial and reading skills. A sample of males and females volunteer to participate and are given 10 minutes to work on a 50-word puzzle. The number of words correctly recognized is recorded for each subject, and the resulting data are as follows:

Males Females

12          15

8            12

9            11

11          18

10          13

12          14

7            17

Conduct the appropriate analysis of these data and determine whether there are any significant differences.

13. A college student is interested whether there is a difference between male and female students in the amount of time spending working out each week. The student gathers information from a random sample of male and female students on her campus. Amount of time spend working out is normally distributed. The data appear below.

Males Females

7         5

5         9

9         8

10       3

6         10

2          5

4          9

a) What statistical test should be used to analyze these data?

b) Identify Ho and Ha for this study.

c) Conduct the appropriate analysis.

d) Should Ho be rejected? What should the researcher conclude?

e) If significant compute the effect size and interpret this.

14. A student is interested in whether students who study with others devote as much attention to their studies as do students who study alone. He believes those who study alone devote more attention to their studies. He randomly assigns participants to either group or individual study conditions and has them read and study the same passage of information for the same amount of time. Participants are then given the same 10-item test on the material. Their scores appear below. Scores on the test represent interval/ratio data and are normally distributed.

Group Alone

6            10

5            9

6            7

5            7

6            6

6            6

7            8

8            6

5            9

a) What statistical test should be used to analyze these data?

b) Identify H0 and Ha for this study.

c) Conduct the appropriate analysis.

d) Should H0 be rejected? What should the researcher conclude?

e) If significant, compute the effect size and interpret this.

15. A researcher believes exercise reduces anxiety in women. She identifies a group of women who had not exercised before but are now planning to begin exercising. She gives them a 50-item anxiety inventory before they begin exercising and administers it again after 6 months of exercising. The anxiety inventory is measured on an interval scale and higher numbers indicate higher anxiety. In addition, scores on the inventory are normally distributed. The scores appear below.

Before After

46         44

41         40

42         39

47         46

43         42

45         43

a) What statistical test should be used to analyze these data?

b) Identify Ho and Ha for this study.

c) Conduct the appropriate analysis.

d) Should Ho be rejected? What should the researcher conclude?

e) If significant, compute the effect size and interpret this.

16. A researcher is interested in comparing the self-esteem of students who volunteer for community service versus those who do not. The researcher assumes that those who complete community service will have higher self-esteem scores. Self-esteem scores tend to be skewed (not normally distributed). The self-esteem scores appear below. Higher scores indicate higher self-esteem levels.

No Community

Service Community Service

33                   41

41                   48

54                   61

13                   72

22                   83

26                   55

a) What statistical test should be used to analyze these data?

b) Identify H0 and Ha for this study.

c) Conduct the appropriate analysis.

d) Should H0 be rejected? What should the researcher conclude?

17. You noticed in a training class that it appears that more men tend to sit near the door and more women opposite the door. In order to determine whether this difference is significant, you collect data on the seating preferences for the students in your class. The data appears below:

Males Females

Near the Door             25       14

Opposite the Door     12        20

a) What is the statistical test that should be used to analyze these data?

b) Identify Ho and Ha for this study.

c) Conduct the appropriate analysis.

d) Should Ho be rejected? What should the researcher conclude?

18. Explain when it should be appropriate to use a t test versus a one-way analysis of variance.

19. What is the Bonferroni adjustment? What would the Bonferroni adjustment be for a study with four groups for which a researcher decided to use t-tests?

20. If the null hypothesis is true, what value should we expect for the F-ratio? Why?

21. When and why is it necessary to use post-hoc tests?

22. Provide the factorial notation for the following experimental design. Two independent variables:

1. Crust Type (thick, thin, pan, and hand-tossed)

2. Topping Type (plain, sausage, pepperoni, veggie, ham, and everything)

23. How many main effects and interactions could you have in a 4 x 6 factorial design?

24. Explain the difference between correlational, quasi-experimental, and true-experimental design.

25. Why is an ABAB reversal design better than an ABA reversal design?

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