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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Question 1: The most appropriate test for these data and hypothesis is c. Independent t-test.
Question 2: The null hypothesis is c. CBT = Control.
Question 3: The observed value for the chosen test statistic is c. 2.846.
Question 4: The critical value for this hypothesis (using an alpha = .10) is c. 1.761.
Question 5: The researcher can conclude that c. Students in the computerized algebra training group had significantly higher test scores than students who received standard teaching methods.
Question 6: The most appropriate test to use for testing the hypothesis in the ACT study is b. Correlated samples t-test (or a dependent t-test).
Question 7: The alternative hypothesis for the ACT study is a. ACT1 > ACT2, where 1 = pretest and 2 = posttest.
Question 8: The value of the observed test statistic for the ACT study is b. -1.172 or 1.172.
Question 9: Examples of a non-independent t-test would be d. All of the above.
Question 10: The greatest statistical power for a study occurs when d. The sample is large and the heterogeneity is small.
Question 11: The effect size for the difference between the treatment and control groups using delta is c. 2.23.
Question 12: In order to have at least an 80% probability of identifying an effect size of .20, if it exists, a sample size of approximately 262 students will be needed.
Question 13: The effect size for this study (using delta) is a. .32.
Question 14: The researchers in the previous weight loss study would not have had sufficient power to identify an effect size of .30 if they were using a one-tailed alpha = .01. A sample of 145 would be needed for a power = .90.
Question 15: Compute the appropriate test-statistic and round to 2 decimal places.
Question 16: The difference in the weight loss experienced by the two Weight Loss Program groups would not be larger than what we would expect by chance. The observed test statistic is smaller than the critical value of 1.96.
Question 17: In order to increase the power of the study, the researcher could a. increase the sample size of the two groups and c. change the alpha level to .001.
Question 18: 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.
To answer these questions, we need to understand the research design, data, and statistical tests appropriate for the given scenarios. Let's go through each question step by step:
Question 1:
The researcher is comparing the effectiveness of two teaching methods for algebra. The appropriate test for this scenario is an independent t-test because the two groups are independent and the data is continuous.
Answer: c. Independent t-test
Question 2:
The null hypothesis is the statement that there is no difference between the two teaching methods.
Answer: c. CBT = Control
Question 3:
The observed value for the chosen test statistic is not given in the question.
Question 4:
To determine the critical value for an alpha of 0.10, we need to look it up in a t-table or use statistical software. The critical value for this scenario is approximately 1.761.
Answer: c. 1.761
Question 5:
Based on the results of the test, the researcher can conclude that there is a significant difference in the performance of students receiving the computer training compared to those receiving standard teaching methods.
Answer: c. Students in the computerized algebra training group had significantly higher test scores than students who received standard teaching methods.
Question 6:
For the ACT study, the appropriate test is a correlated samples t-test because the same subjects are being tested before and after the treatment.
Answer:
b. Correlated samples t-test
Question 7:
The alternative hypothesis for the ACT study is that the post-treatment scores (ACT 2nd) will be greater than the pre-treatment scores (ACT 1st).
Answer:
a. ACT1 > ACT2, where 1 = pretest and 2 = posttest
Question 8:
The value of the observed test statistic for the ACT study is not given in the question.
Question 9:
Examples of non-independent t-tests include scenario "a" and scenario "c" mentioned in the options.
Answer:
d. All of the above
Question 10:
The greatest statistical power for a study occurs when the sample is large and the heterogeneity is small.
Answer:
d. The sample is large and the heterogeneity is small.
Question 11:
To compute the effect size using delta, we need to calculate the mean difference between the treatment and control groups and divide it by the pooled standard deviation.
Answer: The effect size using delta is not provided in the question.
Question 12:
To determine the sample size needed for a study with a specified effect size, alpha level, and desired power, we can use a power analysis. In this case, an effect size of 0.20 is important to detect, and we want a power of 80%.
Answer:
b. Approximately 155 students
Question: 13
The effect size for this study can be determined by calculating Cohen's d, which is the difference in means divided by the pooled standard deviation.
Answer:
a. 0.32
Question: 14
To determine if the researchers in the weight loss study had sufficient power to identify an effect size of 0.30, we need to calculate the appropriate sample size using power analysis.
Answer:
d. No, a sample of 145 would be needed for a power = .90.
Question: 15
To determine if the weight loss drug is significantly more effective than diet alone, we need to perform a statistical test. Since the question does not explicitly state the type of test to be used, we cannot compute the appropriate test statistic.
Question: 16
Based on the given choices, we cannot determine if the observed test statistic is larger or smaller than the critical value for a one-tailed test.
Question: 17
To increase the power of a study, we can increase the sample size and/or use a higher alpha level.
Answer:
a. Increase the sample size of the two groups
c. Change the alpha level to .001
Question: 18
To determine the statistical conclusion using a directional alternative hypothesis test with an alpha = .10, we need to compare the observed test statistic with the critical value.
Answer:
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.