Question

Question 1:

Researchers were interested in the effect of sleep on memory consolidation. Twenty-four participants were randomly assigned to either a “Sleep” or “No-Sleep” group, such that there were 12 participants in each group. On the first day, all participants were flashed pictures of 15 different objects on a computer screen and asked to remember as many objects as possible. That night, the “Sleep” group got an ordinary night’s sleep. The “No-Sleep” group was kept awake until the second night. All participants got an ordinary night’s sleep on the second and third nights. On the fourth day, all participants were tested to see how many of the original 15 objects they remembered. Conduct an independent samples t-test, two-tailed, alpha = .05.

Sleep   NoSleep
14   8
13   9
8   6
9   13
11   7
10   9
9   10
13   12
12   8
11   11
14   9
13   12

a. Write the null hypothesis in symbols and words

b. Write the alternative hypothesis in symbols and words

c. By hand, calculate the degrees of freedom. Show calculation

d. Use the t-test function in R to obtain the test statistic and p-value

e. Make a decision about the null using the p-value approach

f. Write the conclusion in APA style

g. Using R, compute and report the 95% CI.

h. Interpret the 95% CI.

i. Using the CI, make a decision about the null hypothesis. Be sure to explain your reasoning.

j. Does this agree with your decision from part (e)?

Answer 1

R code:

sleep=c(14,13,8,9,11,10,9,13,12,11,14,13)
Nosleep=c(8,9,6,13,7,9,10,12,8,11,9,12)
t.test(sleep,Nosleep, var.equal=TRUE, paired=FALSE)

Output:

Two Sample t-test

data: sleep and Nosleep
t = 2.2254, df = 22, p-value = 0.03662
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.1304937 3.7028397
sample estimates:
mean of x mean of y
11.41667 9.50000
The value of test statistic=2.2254, p-value=0.03662

e. Since p-value<0.05 so we reject H₀ at level 0.05.

f. There is significant effect of sleep on memory consolidation.

g. 95 percent confidence interval:
(0.1304937, 3.7028397)

h. We are 95% confident that the difference between true mean of these two groups falls in (0.1304937, 3.7028397).

i. Since 95% C.I. does not contain zero so we we reject H₀.

j. Yes.