Question

M8 Assessment: Testing Difference between Means (t-tests)

Concluding Statements for t-tests: These statements should always reflect back on the study and outcome, or results. Practice writing statements for each outcome in your practice problems and homework. Use the following example write-up for problems 7-10.

• An [independent samples or dependent sample] t-test was conducted to determine [state the purpose of the study]. The results revealed [a significant or no significant] difference between [state the groups and/or independent variable] on [state the dependent variable] (t ([degrees of freedom]) = [enter computed value for t], p [< or >]* .05). In fact, [state each group and explain how the means compare].

*The less than (<) sign means the results are significant and the greater than (>) sign means the results are not significant.

Questions 1-3: Dr. Mackintosh believes a new olfactory therapy would be more successful in promoting weight loss among obese patients. His patients are first weighed and then randomly assigned to olfactory therapy, dance therapy, or a control condition. At the end of the three weeks, the amount of weight lost is recorded. The results indicate no significant difference in the amount of weight lost between the three conditions.

1. Identify the independent variable along with each level and the dependent variable.

2. If true differences existed between the conditions, but they were not detected, what kind of error occurred?

3. If differences in conditions were detected, but did not really exist, what kind of error occurred?

Questions 4-6: A sleep researcher wants to determine whether a new pillow might reduce snoring amongst patients with this type of sleep apnea. Participants are randomly assigned to use the new pillow or a control condition (regular pillow). Their sleep behavior is recorded on audiotape with time snoring. The findings indicate significantly less snoring takes place with the new pillow.

4. Identify the independent variable (and categories) and the dependent variable.

5. Explain a Type I error in terms of this study.

6. Explain a Type II error in terms of this study.

Questions 7-10: Compute the appropriate t-test.

7. A researcher interested in eating behavior wants to determine if scary movies cause people to eat more popcorn than musicals. You randomly assign 10 participants to a group that watches a scary movie (Psycho) and another 10 participants to a group that watches a musical (The Sound of Music). At the beginning of the movie, you give each participant a tub of 84 pieces of popcorn and tell each person not to share their popcorn with anyone. At the end of the movie, you measure the number of pieces of popcorn eaten by each participant. The data are shown below. Based on the results of this t-test, state the conclusions about the difference between the pieces of popcorn eaten by subjects viewing a scary movie versus a musical.

Scary Musical

   X Y      

  45 32

  67 38

  69 33

  56 49

  73 44

  56 60

  63 48

  84 36

  49 23

  56 39

8. An education researcher is interested in the ability of preschool children to solve math story problems. He wants to see if the method of presentation, either as verbal story problems or as visual story problems, makes a difference in preschoolers' abilities to solve the problems correctly. In an example of the verbal condition, a child is asked, "Two birds are sitting on a fence; two more birds fly down and join them. How many birds are on the fence altogether?" In an example of the nonverbal, visual equivalent of this problem, the experimenter presents the child with a picture of two birds on the fence with two birds in the process of landing on the fence and then asks the child, "How many birds are on the fence altogether?" In both conditions, the child responds orally. Shown below is the number of correct answers out of 10 problems for each child. What conclusions about the difference between a preschooler's ability to solve simple math problems presented either verbally or nonverbally can be made from these results?

Child Verbal Nonverbal

C. J. 3 6

F. K. 5 8

M. O. 7 9

I. M. 4 8

G. G. 2 4

K. T. 1 1

B. W. 4 3

M. B. 2 8

9. Education researchers were interested in whether the number of close friends changes between the time students enter college and the beginning of their second year of college. A sample of 12 (entering) first-year students was used to examine the question. Data for this sample are shown below.

Answer 1

1. The independent variable=Conditions and levels are  olfactory therapy, dance therapy and control condition. The dependent variable=Weight lost.

2 If true differences existed between the conditions, but they were not detected, so Type II error is committed.

3. If differences in conditions were detected, but did not really exist, so Type I error is committed.

4. The independent variable=pillow type, levels=new pillow and regular pillow. The dependent variable=snoring

5. Type I error=The findings indicate less snoring takes place with the new pillow but in reality it is not true.

6. Type II error=The findings do not indicate less snoring takes place with the new pillow but in reality it is not true.

7.

Minitab output:

Two-Sample T-Test and CI: Scary, Musical

Two-sample T for Scary vs Musical

N Mean StDev SE Mean
Scary 10 61.8 11.8 3.7
Musical 10 40.2 10.5 3.3

Difference = mu (Scary) - mu (Musical)
Estimate for difference: 21.60
95% lower bound for difference: 12.97
T-Test of difference = 0 (vs >): T-Value = 4.34 P-Value = 0.000 DF = 18
Both use Pooled StDev = 11.1285

Since P-value=0.000<0.05 so we reject H0 at 5% level of significance and there is sufficient evidence to conclude that scary movies cause people to eat more popcorn than musicals.