Please complete by Thursday December 3rd. Answers are included below. If you cannot get the correct answer, please e-mail Mariela.
1- The average age for licensed drivers in the county is µ = 40.3 years with a standard deviation of σ = 13.2 years.
a-A researcher obtained a random sample of n = 16 parking tickets and computed an average age of M = 38.9 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = 16 people is a representative sample of licensed drivers?
2- There is some evidence that REM sleep, associated with dreaming, may also play a role in learning and memory processing. For example, Smith and Lapp (1991) found increased REM activity for college students during the exam periods. Suppose that REM activity for a sample of n = 16 students during the final exam period produced an average score of M = 143. Regular REM activity for the college population averages µ = 110 with a standard deviation of σ = 50. The population distribution is approximately normal.
a-Do the data from this sample provide evidence for a significant increase in REM activity during exams? Use a one-tailed test with α= .01.
b-Compute Cohen’s d to estimate the size of the effect.
c-Write a sentence describing the outcome of the hypothesis and the measure of effect size as it would appear in a research report.
3- A psychologist has prepared an “Optimism Test” that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future- the higher the score, the more optimistic the class. Last year’s class had a mean score of µ = 15. A sample of n = 9 seniors from this year’s class was selected and tested. The scores for these seniors are 7,12,11,15,7,8,15,9,6. On the basis of this sample, can the psychologist conclude that this year’s class has a different level of optimism than last year’s class? (use two tails, α= .05)
Answers:
1) a. With a standard error of σM = 3.3, M = 38.9 corresponds to z = –0.42 and p = 0.3372. This is not an unusual sample. It is representative of the population.
2) 12. a. The null hypothesis states that there is no increase in REM activity, µ ≤ 110. The critical region consists of z-scores beyond z = 2.33. For these data, the standard error is 12.5 and z = 33/12.5 = 2.64. Reject H0. There is a significant increase in REM activity.
b. Cohen’s d = 33/50 = 0.66.
c. The results show a significant increase in REM activity for college students during exam periods, z = 2.64, p < .01, d = 0.66.
3)M = 10, SS = 94 , critical t value = +-2.306, df = 8, s2 = 11.75, sM = 1.14, t = -4.39. reject the null hypothesis. There is a significant difference in levels of optimism between this year’s and last year’s graduating class. Senior from this year’s class felt significantly less optimistic when compared to the last cohort.