researcher suspects that, on average, those who are married have a higher household income than their unmarried counterparts. An independent samples t-test has been conducted to empirically examine whether the research’s gut feeling is true or not (alpha = 0.05). The two relevant variables for this problem are: marital and income (see the attached screenshot). Technically speaking, please report both t-statistic and its associated p-value for the group mean difference test (i.e., an independent samples t-test) Question 1: Using the screenshot image, please examine the following null hypothesis (please do state the null hypothesis here) and the alternative hypothesis (please state the null hypothesis here). We employed an independent samples t-test to examine the above null hypothesis, and found the t-statistic and the corresponding p-value to be _____________ and _____________, respectively. As the p-value is (or is not) smaller than the critical alpha, the null hypothesis should be (or should not be) rejected at the 0.05 alpha level. In other words, the married respondents and their unmarried counterparts have approximately the same (or have a significantly different) average income (see attached screenhot image).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
icon
Related questions
Question

researcher suspects that, on average, those who are married have a higher household
income than their unmarried counterparts. An independent samples t-test has been conducted to empirically examine whether the research’s gut feeling is true or not (alpha = 0.05). The two relevant variables for this problem are: marital and income (see the attached screenshot).

Technically speaking, please report both t-statistic and its associated p-value for the group mean
difference test (i.e., an independent samples t-test)

Question 1: Using the screenshot image, please examine the following null hypothesis (please do state the null hypothesis here) and the alternative hypothesis (please state the null hypothesis here). We employed an independent samples t-test to examine the above null hypothesis, and found the t-statistic and the corresponding p-value to be _____________ and _____________, respectively. As the p-value is (or is not) smaller than the critical alpha, the null hypothesis should be (or should not be) rejected at the 0.05 alpha level. In other words, the married respondents and their unmarried counterparts have approximately the same (or have a significantly different) average income (see attached screenhot image).

Household income in
thousands
Household income in
thousands
Household income in
thousands
Group Statistics
Marital status
Unmarried
Married
N
741
759
Equal variances assumed
Equal variances not
assumed
Cohen's d
Hedges' correction
Glass's delta
Mean
69.1053
72.2740
Std. Deviation
85.40495
86.69930
F
Levene's Test for Equality of
Variances
86.06233
86.10545
86.69930
Independent Samples Test
Independent Samples Effect Sizes
.562
Standardizer Point Estimate
-.037
-.037
-.037
Std. Error Mean
3.13743
3.14699
Sig.
a. The denominator used in estimating the effect sizes.
Cohen's d uses the pooled standard deviation.
Hedges' correction uses the pooled standard deviation, plus a correction factor.
Glass's delta uses the sample standard deviation of the control group.
.453
t
df
-.713
1498
-.713 1497.879
95% Confidence Interval
Lower
Upper
-.138
-.138
-.138
.064
.064
.065
Significance
One-Sided p
.238
.238
t-test for Equality of Means
Two-Sided p
.476
.476
Mean
Difference
-3.16878
-3.16878
Std. Error
Difference
4.44456
4.44376
95% Confidence Interval of the
Difference
Lower
-11.88700
-11.88543
Upper
5.54944
5.54787
Transcribed Image Text:Household income in thousands Household income in thousands Household income in thousands Group Statistics Marital status Unmarried Married N 741 759 Equal variances assumed Equal variances not assumed Cohen's d Hedges' correction Glass's delta Mean 69.1053 72.2740 Std. Deviation 85.40495 86.69930 F Levene's Test for Equality of Variances 86.06233 86.10545 86.69930 Independent Samples Test Independent Samples Effect Sizes .562 Standardizer Point Estimate -.037 -.037 -.037 Std. Error Mean 3.13743 3.14699 Sig. a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control group. .453 t df -.713 1498 -.713 1497.879 95% Confidence Interval Lower Upper -.138 -.138 -.138 .064 .064 .065 Significance One-Sided p .238 .238 t-test for Equality of Means Two-Sided p .476 .476 Mean Difference -3.16878 -3.16878 Std. Error Difference 4.44456 4.44376 95% Confidence Interval of the Difference Lower -11.88700 -11.88543 Upper 5.54944 5.54787
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill