Question

1. In a study designed to measure various aspects of multicultural sensitivity, simple random samples of 15 male and 15 female clinical psychologists were given several tests. On one of the tests, the two sets of sample scores were:

         Male Female

63      58

71      62

68      65

60      63

69      62

70      58

69      62

72      66

69      60

63      61

58      60

65      70

65      64

70      67

74      63

Do these scores indicate a difference between men and women with respect to this aspect of multicultural sensitivity? Begin by identifying a statement to be tested, the random variable(s) involved and any assumptions you make about them, level of significance, the statistical hypotheses to be tested, the test statistic and critical region. Then, either by hand or using SPSS (provide all SPSS output you use), do the hypothesis test, make a decision about the hypotheses, and draw conclusions as to whether there are differences based on gender.

Answer 1

Given that,
mean(x)=67.0667
standard deviation , s.d1=4.5586
number(n1)=15
y(mean)=62.733
standard deviation, s.d2 =3.3051
number(n2)=15
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.145
since our test is two-tailed
reject Ho, if to < -2.145 OR if to > 2.145
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =67.0667-62.733/sqrt((20.78083/15)+(10.92369/15))
to =2.981
| to | =2.981
critical value
the value of |t α| with min (n1-1, n2-1) i.e 14 d.f is 2.145
we got |to| = 2.98088 & | t α | = 2.145
make decision
hence value of | to | > | t α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.9809 ) = 0.01
hence value of p0.05 > 0.01,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.981
critical value: -2.145 , 2.145
decision: reject Ho
p-value: 0.01
we have enough evidence to support the claim that difference between men and women with respect to this aspect of multicultural sensitivity