1 A sleep researcher conducts an experiment where she random

1. A sleep researcher conducts an experiment where she randomly assigns 60 participants to receive one of three levels of sleep deprivation, sleep deprived for 24 hours (SD24), sleep deprived for 48 hours (SD48), and no sleep deprivation (SD0). After the experimental condition (sleep deprivation), the participants are given an auditory vigilance task and the correct percentages are calculated. The means for the three groups are SD0=76.6, SD24=61.8, SD48=48.6. The ANOVA F test had a p-value=.003. What is your statistical conclusion?

a. The group with the most sleep deprivation had a lower mean than the other two groups

b. The mean for the non-sleep deprived group performed significantly better than the other two groups.

c. The mean for the SD0 group was significantly greater than the mean for the SD24 group which was significantly greater than the mean for the SD48 group

d. The means for the three conditions were not all equal

2. To test whether Internet use is associated with depression, we asked a random sample of Internet users to record their hours of Internet use for one week and then measured their depression score (range 0-30) at the end of that week. What test would be most appropriate for this study?

a. matched pairs t-test

b. two-sample t-test

c. ANOVA

d. chi-squared test for independence

e. inference for regression

3. A researcher randomly assigned 160 subjects into one of two groups: Atkins diet or Weight Watchers. The response variable was pounds lost after 6 weeks. The t-test results showed a p-value=.51. What can be concluded?

a. Neither of the diets were effective in reducing weight

b. There was not evidence to suggest the diets differed in mean weight loss.

c. The means weight loss was better for the Weight Watcher group

d. Descriptive data are needed before an accurate conclusion can be made.

Solution

ANSWER IN BOLD.

1. The means for the three groups are SD0=76.6, SD24=61.8, SD48=48.6. The ANOVA F test had a p-value=.003. What is your statistical conclusion?

The auditory vigiilance task across the three levels of sleep deprivation are significantly different from each other.

a. The group with the most sleep deprivation had a lower mean than the other two groups

b. The mean for the non-sleep deprived group performed significantly better than the other two groups.

c. The mean for the SD0 group was significantly greater than the mean for the SD24 group which was significantly greater than the mean for the SD48 group

d. The means for the three conditions were not all equal

Only d statement can be asserted. Other tests need further deepdive of the contrasts.

2.

a. matched pairs t-test

b. two-sample t-test

c. ANOVA

d. chi-squared test for independence

e. inference for regression

3.

a. Neither of the diets were effective in reducing weight

b. There was not evidence to suggest the diets differed in mean weight loss.

c. The means weight loss was better for the Weight Watcher group

d. Descriptive data are needed before an accurate conclusion can be made.