Statistical significance is found in a study, but the effect in reality is very

Question

Statistical significance is found in a study, but the effect in reality is very small (i.e., there was a very minor difference in attitude between men and women). Were the results meaningful? An independent samples t test was conducted to determine whether differences exist between men and women on cultural competency scores. The samples consisted of 663 women and 650 men taken from a convenience sample of public, private, and non-profit organizations. Each participant was administered an instrument that measured his or her current levels of cultural competency. The © 2016 Laureate Education, Inc. Page 2 of 2 cultural competency score ranges from 0 to 10, with higher scores indicating higher levels of cultural competency. The descriptive statistics indicate women have higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD = 2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are more culturally competent than are men. These results tell us that gender-specific interventions targeted toward men may assist in bolstering cultural competency.

Explanation / Answer

Given that,
mean(x)=9.2
standard deviation , s.d1=3.2
number(n1)=663
y(mean)=8.9
standard deviation, s.d2 =2.1
number(n2)=650
null, Ho: u1 < u2
alternate, H1: u1 > u2
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.647
since our test is right-tailed
reject Ho, if to > 1.647
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =9.2-8.9/sqrt((10.24/663)+(4.41/650))
to =2.012
| to | =2.012
critical value
the value of |t | with min (n1-1, n2-1) i.e 649 d.f is 1.647
we got |to| = 2.01213 & | t | = 1.647
make decision
hence value of | to | > | t | and here we reject Ho
p-value:right tail - Ha : ( p > 2.0121 ) = 0.02231
hence value of p0.05 > 0.02231,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, indicating that women are more culturally competent than are men H1: u1 > u2
test statistic: 2.012
critical value: 1.647
decision: reject Ho
p-value: 0.02231
we have evidence to support that women are more culturally competent than are men

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