# Statistics

Question 1

Use the following research question and data for questions 1 - 6.

A researcher is examining the effects of a computer-based training program designed to teach algebra. The researcher randomly selects subjects for two groups and gives one group the computer training and the other group the standard teaching methods to see if the two methods differ in their effectiveness. The following scores are from the subjects' final test.
CBT Control
54 56
57 45
50 47
55 46
52 47
51 39
54 47
43 49

What test is most appropriate for these data and hypothesis?
a. Chi-square

b. Correlated t-test (or dependent t-test)

c. Independent t-test

d. Pearson's r

Question 2

What is the null hypothesis?
a. CBT > Control

b. CBT < Control

c. CBT = Control

d. none of the above

Question 3

What is the observed value for the chosen test statistic?

a. 0.24

b. 2.23

c. 2.846

d. 5.00

Question 4

What is the critical value for this hypothesis (using an alpha = .10)?

a. 1.345

b. 1.415

c. 1.761

d. 1.895

Question 5

The researcher can conclude that:
a. There is no significant difference in the performance of students receiving the computer training as computer to the students receiving standard teaching methods.

b. Every student who used the computer program scored higher than any student who did not use the program.

c. Students in the computerized algebra training group had significantly higher test scores than students who received standard teaching methods.

d. Both b and c

Question 6

Use the following research question and data for questions 7 - 10.

A group of researchers has developed a method that they hypothesize will improve ACT scores. They randomly selected nine students to participate in their study. The nine students were administered an ACT test, trained using the new treatment program, and then administered another ACT test. The following data are their scores:

Subject ACT 1st ACT 2nd
1 20 19
2 20 20
3 24 21
4 24 24
5 24 22
6 19 17
7 17 15
8 18 16
9 20 18

Which test is most appropriate to use for testing the hypothesis?
a. Chi-square

b. Correlated samples t-test (or a dependent t-test)

c. Independent t-test

d. Pearson's r

Question 7

What is the alternative hypothesis for the ACT study?
a. ACT1 > ACT2 where 1 = pretest and 2 = posttest

b. ACT1 < ACT2 where 1 = pretest and 2 = posttest

c. ACT1 = ACT2

Question 8

What would be the value of your observed test statistic for the ACT study?

a. -0.940 or 0.940

b. -1.172 or 1.172

c. -4.603 or 4.603

d. none of the above

Question 9

Which of the following would be examples of a non-independent t-test?
a. Comparing college algebra exam scores of two groups of college students that were selected by dividing pairs of students matched on IQ scores into two groups.

b. Randomly assigning two sisters to one of two groups in order to investigate the effectiveness of a two weight training methods on upper body strength.

c. An investigation of a change in cholesterol levels by measuring participants' cholesterol levels prior to medication and measuring their cholesterol again after 6 months on a new medication.

d. All of the above

Question 10

The greatest statistical power for a study occurs when:
a. The sample is small and heterogeneity is large.

b. The sample is small and heterogeneity is small.

c. The sample is large and the heterogeneity is large.

d. The sample is large and the heterogeneity is small.

Question 11

Using the data in question 1 (addressing the use of computer-based training to teach algebra), compute the effect size for the difference between the treatment and control groups using delta.
a. 0.23

b. 1.07

c. 2.23

d. 5

Question 12

You are planning a study on the effectiveness of a new program for preventing high school students from dropping out of school. You have determined that a relatively small effect size of .20 would be important to identify. Using an alpha of .05 (and a directional alternative hypothesis - one-tailed test), you want your study to have at least an 80% probability of identifying an effect size of .20, if it exists. What size of a sample will you need?
a. approximately 62 students

b. approximately 155 students

c. approximately 214 students

d. approximately 262 students

Question 13

You are reading an article about the effectiveness of a weight loss drug. The researchers randomly assigned people to one of two groups: the treatment group who receives the weight loss drug while they follow a diet program and a control group that receives a placebo while following the same diet program. The dependent variable is the number of pounds lost in one month. They report the following descriptive statistics:
N Mean Std Dev
Treatment Group (Weight Loss Drug)
10 5.2 1.93
Control Group(Placebo) 10 4.6 1.90

What would be the effect size for this study (using delta)?
a. .32

b. .60

c. 1.90

d. 1.93

Question 14

Would the researchers in the previous weight loss study have had sufficient power (use Power = .90) to identify an effect size of .30 if they were using a one-tailed alpha = .01?
a. Yes, a sample size of 10 would be sufficient for a power of .90

b. No, a sample of 95 would be needed to have a power of .90

c. No, a sample of 117 would be needed for a power = .90

d. No, a sample of 145 would be needed for a power = .90

Question 15

The raw data from the Weight Loss study are provided below. Determine if the Weight Loss Drug is significantly more effective than diet alone in reducing weight. The dependent variable is the number of pounds lost in one month.
Treatment Group Control Group
(Weight Loss Drug + Diet) (Diet Only)
7 5
6 8
6 6
4 5
5 3
2 2
8 6
7 4
3 2
4 5
Compute the appropriate test-statistic and round to 2 decimal places.

Question 16

Would the difference in the weight loss experienced by the two Weight Loss Program groups be larger than what we would expect by chance? (i.e., is there a significant difference using a one-tailed alpha of .01)

a. No, the observed test statistic is smaller than the critical value of 1.645

b. No, the observed test statistic is smaller than the critical value of 1.96

c. No, the observed test statistic is smaller than the critical value of 2.55

d. Yes, the observed test statistic is larger than the critical value

Question 17

Another researcher is going to replicate the Weight Loss study. She wants to design a study that will have a substantially larger probability of finding an effect size of .30 than the previous study had. Which of the following things could she do to increase the power of the study? Check ALL that apply. You may have more than one answer on this question!
a. increase the sample size of the two groups

b. change the alpha level to .10

c. change the alpha level to .001

d. use a non-directional alternative hypothesis rather than a directional hypothesis

Question 18

What would be your statistical conclusion using a directional alternative hypothesis test with an alpha = .10?
a. With the critical value of 1.397, we conclude that we should reject the null hypothesis and conclude that the ACT program is effective in significantly increasing ACT scores.

b. With the critical value of 1.397, we conclude that we should retain the null hypothesis because the observed test statistic indicates that there was actually a decrease in ACT scores rather than an increase in ACT scores. Thus, because we were conducting a directional test, we would have to conclude that the evidence does not support the hypothesis that the ACT program is effective in increasing student ACT scores.

c. With the critical value of 1.86, we conclude that we should reject the null hypothesis and conclude that the ACT program is effective in significantly increasing ACT scores.

d. With the critical value of 1.86, we conclude that we should retain the null hypothesis because the observed test statistic indicates that there was actually a decrease in ACT scores rather than an increase in ACT scores. Thus, because we were conducting a directional test, we would have to conclude that the evidence does not support the hypothesis that the ACT program is effective in increasing student ACT scores.

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