In a study designed to measure various aspects of multicultural sensitivity, sim
ID: 2934321 • Letter: I
Question
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
65 65
71 70
67 58
67 64
69 61
61 63
55 59
71 71
72 72
69 59
62 65
65 67
79 65
64 67
65 66
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.
i would love to have this question answer by hand calculation for my understanding. thanks
Explanation / Answer
Solution:
Here, we have to use two sample t test for testing the significant difference between two population means. The null and alternative hypotheses for this test are given as below:
Null hypothesis: H0: There is no any statistically significant difference between men and women with respect to this aspect of multicultural sensitivity.
Alternative hypothesis: Ha: There is a statistically significant difference between men and women with respect to this aspect of multicultural sensitivity.
Symbolically, the null and alternative hypotheses are given as below:
H0: µmale = µfemale Vs Ha: µmale µfemale
This is a two tailed test.
We assume 5% level of significance for this test.
= 0.05
The test statistic formula is given as below:
t = (X1bar – X2bar) / sqrt[Sp2 (1/N1)+(1/N2)] where
Sp2 = [(N1 – 1)S1^2 + (N2 – 1)S2^2]/[N1 + N2 – 2]
From the given data for samples, we have
X1bar = 66.8
X2bar = 64.8
S1 = 5.57033
S2 = 4.312772
N1 = 15
N2 = 15
DF = N1 + N2 – 2 = 15 + 15 – 2 = 28
Sp2 = [(15 – 1)* 5.57033^2 + (15 – 1)* 4.312772^2]/[15 + 15 – 2]
Sp2 = 24.8143
t = (66.8 - 64.8) / sqrt(24.8143*((1/15)+(1/15)))
t = 1.099536405
Critical values = -2.0484 and 2.0484 (By using t-table)
P-value = 0.2809 (by using t-table)
P-value = 0.2809 > = 0.05
So, we do not reject the null hypothesis that there is no any statistically significant difference between men and women with respect to this aspect of multicultural sensitivity.
There is sufficient evidence to conclude that there is no any statistically significant difference between men and women with respect to this aspect of multicultural sensitivity.
There is insufficient evidence to conclude that there is a statistically significant difference between men and women with respect to this aspect of multicultural sensitivity.
Excel output is given as below:
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
15
Sample Mean
66.8
Sample Standard Deviation
5.57033
Population 2 Sample
Sample Size
15
Sample Mean
64.8
Sample Standard Deviation
4.312772
Intermediate Calculations
Population 1 Sample Degrees of Freedom
14
Population 2 Sample Degrees of Freedom
14
Total Degrees of Freedom
28
Pooled Variance
24.8143
Standard Error
1.8189
Difference in Sample Means
2.0000
t Test Statistic
1.0995
Two-Tail Test
Lower Critical Value
-2.0484
Upper Critical Value
2.0484
p-Value
0.2809
Do not reject the null hypothesis
SPSS output is given as below:
Group Statistics
Gender
N
Mean
Std. Deviation
Std. Error Mean
Sensitivity
Male
15
66.8000
5.57033
1.43825
Female
15
64.8000
4.31277
1.11355
Independent Samples Test
Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
Sensitivity
Equal variances assumed
.447
.509
1.100
28
.281
2.00000
1.81895
-1.72595
5.72595
Equal variances not assumed
1.100
26.348
.281
2.00000
1.81895
-1.73650
5.73650
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.05
Population 1 Sample
Sample Size
15
Sample Mean
66.8
Sample Standard Deviation
5.57033
Population 2 Sample
Sample Size
15
Sample Mean
64.8
Sample Standard Deviation
4.312772
Intermediate Calculations
Population 1 Sample Degrees of Freedom
14
Population 2 Sample Degrees of Freedom
14
Total Degrees of Freedom
28
Pooled Variance
24.8143
Standard Error
1.8189
Difference in Sample Means
2.0000
t Test Statistic
1.0995
Two-Tail Test
Lower Critical Value
-2.0484
Upper Critical Value
2.0484
p-Value
0.2809
Do not reject the null hypothesis