6. A sociologist interested in cultural differences compared women of two ethinic groups on a Role Approval Index (high scores mean high degrees of approval of one's social role). The results are as follows:
Ethnic Group A: N = 15 M= 55 S2 = 6.5 Ethnic Group B : N = 23 M= 51 S2 = 4.5
If the standard deviation of the distribution of the difference between means is .76, what is the t score?
u mean the z score
Z = (Mean1 - Mean2)/Standard Error of Difference between means
Z = (55-51)/.76
To find the t-score, we can use the formula:
t = (M1 - M2) / (s / sqrt(n))
Where:
M1 = Mean of Ethnic Group A
M2 = Mean of Ethnic Group B
s = Standard deviation of the distribution of the difference between means
n = Sample size (number of participants in each group)
Given:
M1 = 55
M2 = 51
s = 0.76
The sample sizes are given as N = 15 for Ethnic Group A and N = 23 for Ethnic Group B.
Using the formula:
t = (55 - 51) / (0.76 / sqrt(15 + 23))
t = 4 / (0.76 / sqrt(38))
t = 4 / (0.76 / 6.1644)
t = 4 / 0.1234
t ≈ 32.40
Therefore, the t-score is approximately 32.40.