A student decides to conduct a study using a withinsubjects

A student decides to conduct a study using a within-subjects design in order to control for differences in cognitive ability. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. The data appear below. As before, they are measured on an interval ratio scale and are normally distributed.

Music No Music

6          10

7          7

6          8

5          7

6          7

8          9

8          8

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

e. If significant, compute the effect size and interpret.

f. If significant, draw a graph representing the data.

Solution

a) Use the STAT feature and choose 2-Sample T-Test .

b) Ho: the mean scores are equal
    Ha: No Music > Music
    alpha = 0.05
c)

Mean1 =6.57 , Mean2 = 8

SD1 = 1.13 , SD2 =1.15

n1 = 7     , n=7

t-statistic = (8 - 6.57) / sqrt((1.15)^2/7 + (1.13)^2/7) = 2.35

dF = (7-1)+(7-1) =12

p-value = 0.036

d) Since p < 0.05,

REJECT the null hypothesis .... No Music results in significantly better scores.

e) Not significant

f) Not significant