Question

There is some evidence indicating 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 exam periods. Suppose that REM activity for a sample of 16 students during the final exam period produced an average score of M = 143. Regular REM activity for college students averages µ = 110 with a standard deviation of σ  = 50. Do these data provide enough evidence to conclude that REM activity is significantly different during exams? In the provided space, please type in the answers to the following questions

1. Which statistical test would you use to solve this problem?

2. State the null and alternative hypothesis in words.

3. Locate the critical value that defines the critical region.

4. Calculate your statistic.

5. Make a decision with respect to the null hypothesis.

6. Write a concluding sentence in everyday language.

7. Calculate and evaluate Cohen’s d.

Answer 1

Part 1)

We will use Z test, since population standard deviation σ is known.

Part 2)

H0 :- µ = 110
H1 :- µ ≠ 110

Part 3)

Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
Critical region Z < -1.96 OR Z > 1.96

Part 4)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 143 - 110 ) / ( 50 / √( 16 ))
Z = 2.64

Part 5)

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 2.64 > 1.96
Result :- Reject null hypothesis

Part 6)

There is sufficient evidence to conclude that REM activity is significantly different during exams.

part 7

Effect size d = (µ sample - µ populaiton ) / σ

d = ( 143 - 110 ) / 50

d = 0.66 ( effect size is small )