the spss file can be downloaded through this link http://www.mediafire.com/file/
ID: 3173988 • Letter: T
Question
the spss file can be downloaded through this link http://www.mediafire.com/file/p29xzx63694rxsh/QOL.sav
You should consider the following instructions when answering the assignment questions:
For confidence intervals:
Check all assumptions.
Interpret the results.
For testing hypothesis:
State the null and alternative hypotheses.
Check the necessary assumptions.
Report the P-value and the test statistic.
Make a conclusion statement in the words of the original problem.
1.Construct and interpret a 95% confidence interval for the difference between the population proportion of Females and the population proportion of Males who have children .
2.Is there a significant difference between the population proportion of Females and the population proportion of males who have children? Use a = 0.05
3.Is there any significant difference in the Total Social Desirability Scale population means due to Sex? Use a = 0.05 as a level of significance
4.At 5% significance level and using the appropriate non-parametric test, can you conclude that Sex affects Total Social Desirability Scale?
5.Does the data support that Age (5 groups) affects Total Self Esteem Scale? Use a = 0.05
6.If differences exist in (5), use a multiple comparison method to determine which levels of Age (5 groups) differ.
7.Use the non-parametric Kruskal-Wallis test to test the equality of the Total Perceived Stress Scale medians among the 5 Age groups. Use a = 0.05
8.Use Two- Way ANOVA to test the main effects (Sex and Source of Stress) and the Interaction for the response variable Total Mastery Scale. Use = .05
9.Use the Chi-Square test of independence to test the relationship between Having Children and Source of Stress. Use = .05
Explanation / Answer
1. Construct and interpret a 95% confidence interval for the difference between the population proportion of Females and the population proportion of Males who have children.
Solution:
From the given data, we have following information:
Sex * Child Cross tabulation
Count
Child
Total
YES
NO
Sex
MALES
80
104
184
FEMALES
105
149
254
Total
185
253
438
We are given
Confidence level = 95%
Number of items of interest (males) = 80
Sample size = 438
So, p1 = 80/438 = 0.182648402
In same way, we have p2 = 0.239726027
Critical Z value = 1.96
Confidence interval = (p1 – p2) -/+ Z*sqrt((p1q1/n1)+(p2q2/n2))
Confidence interval = (0.1826 – 0.2397) -/+ 1.96*sqrt((0.1826*(1 – 0.1826)/438)+(0.2397*(1 – 0.2397)/438))
Confidence interval = -0.05707763 -/+ 0.0539
Lower limit = -0.05707763 - 0.0539 = -0.1110
Upper limit = -0.05707763 + 0.0539 = -0.0032
2. Is there a significant difference between the population proportion of Females and the population proportion of males who have children? Use a = 0.05
Solution:
Null hypothesis: H0: There is no any significant difference in the population proportion of females and the population proportion of males who have children.
Alternative hypothesis: Ha: There is a significant difference in the population proportion of females and the population proportion of males who have children.
We are given
Confidence level = 95%
Number of items of interest (males) = 80
Sample size = 438
So, p1 = 80/438 = 0.182648402
In same way, we have p2 = 0.239726027
Test statistic = Z = = (p1 – p2) / sqrt((p1q1/n1)+(p2q2/n2))
Test statistic = (0.1826 – 0.2397)/sqrt((0.1826*(1 – 0.1826)/438)+(0.2397*(1 – 0.2397)/438))
Test statistic = -2.0695
P-value = 0.0385
Alpha value = 0.05
P-value < Alpha value
So, we reject the null hypothesis that there is no any significant difference in the population proportion of females and the population proportion of males who have children.
We conclude that there is sufficient evidence that there is a significant difference in the population proportion of females and the population proportion of males who have children.
3. Is there any significant difference in the Total Social Desirability Scale population means due to Sex? Use a = 0.05 as a level of significance
Solution:
Null hypothesis: H0: There is no any significant difference in the total social desirability scale population means due to sex.
Alternative hypothesis: Ha: There is a significant difference in the total social desirability scale population means due to sex.
The test by using SPSS is given as below:
Group Statistics
Sex
N
Mean
Std. Deviation
Std. Error Mean
Total social desirability
MALES
183
5.04
2.000
.148
FEMALES
250
5.50
2.056
.130
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
Total social desirability
Equal variances assumed
.047
.828
-2.288
431
.023
-.452
.198
-.841
-.064
Equal variances not assumed
-2.297
398.328
.022
-.452
.197
-.839
-.065
We get p-value = 0.023 < alpha value 0.05, so we reject the null hypothesis that There is no any significant difference in the total social desirability scale population means due to sex.
There is sufficient evidence that there is a significant difference in the total social desirability scale population means due to sex.
4. At 5% significance level and using the appropriate non-parametric test, can you conclude that Sex affects Total Social Desirability Scale?
Solution:
Here, we have to use
Mann-Whitney Test
Null hypothesis: H0: There is no any significant difference in the total social desirability scale population means due to sex.
Alternative hypothesis: Ha: There is a significant difference in the total social desirability scale population means due to sex.
It is given as below
Ranks
Sex
N
Mean Rank
Sum of Ranks
Total social desirability
MALES
183
200.84
36753.50
FEMALES
250
228.83
57207.50
Total
433
Test Statistics
Total social desirability
Mann-Whitney U
19917.500
Wilcoxon W
36753.500
Z
-2.323
Asymp. Sig. (2-tailed)
.020
a. Grouping Variable: Sex
P-value = 0.020 < Alpha = 0.05, so we reject the null hypothesis that there is no any significant difference in the total social desirability scale population means due to sex.
There is sufficient evidence that there is a significant difference in the total social desirability scale population means due to sex.
Sex * Child Cross tabulation
Count
Child
Total
YES
NO
Sex
MALES
80
104
184
FEMALES
105
149
254
Total
185
253
438
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