Question

To investigate whether or not people tend to marry spouses of similar ages or whether husbands tend to be older than their wives, a student gathered age data from a sample of 24 couples, taken from marriage licenses filed in Cumberland County, PA, in June and July 1993.
Diff(H-W)
1
-4
-4
18
2
2
1
1
2
1
0
4
2
-5
7
6
7
2
4
1
-6
1
2
-7
1
16
3
13
2
-1
-1
10
-1
1
0
-4
1
8
-1
-7
1
4
5
3
9
-5
3
-7
2
1
2
-4
0
12
4
13
-1
3
5
3
-2
2
0
2
0
2
13
-1
1
1
2
-3
6
1
1
-5
2
7
-2
-7
-1
1
9
1
-2
-1
3
5
-5
8
1
1
0
2
-2
-7
1
5
7
15
1) Define, in words.
A. The total difference in husband and wife marriage ages in Cumberland County; μd.
B. Average age of men and average age of women; μm and μw.
C. The average difference in husband and wife marriage ages in Cumberland County; μd.
2) Select the appropriate null and alternative hypotheses in the context of the study.
A. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is not 0.
B. Null: The average difference in marriage ages in Cumberland County is not 0. Alt: The average difference in marriage ages is 0.
C. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is less than 0.
D. Null: The average difference in marriage ages in Cumberland County is 0. Alt: The average difference in marriage ages is greater than 0.
3) Select the appropriate null and alternative hypotheses in the context of the study depicted using symbols
A. Null: μd = 0, Alt: μd > 0
B. Null: μd = 0, Alt: μd ≠ 0
C. Null: μd > 0, Alt: μd = 0
D. Null: μd = 0, Alt: μd < 0
4) For the 24 couples, the husbands are, on average, 1.875 years older than their wives (SD = 4.812). Use these statistics and the Theory-Based Inference applet to conduct a test of significance and report the resulting p-value to four decimal places.​
5) Based on the p-value, do you have strong evidence that, on average, husbands are older than their wives in Cumberland County?

Answer 1

Answer:

See explanation below

Explanation:

1) Option C is correct.

The average difference in husband and wife marriage ages in Cumberland County; μd

2) Option D is correct.

Null: The average difference in marriage ages in Cumberland County is 0.

Alt: The average difference in marriage ages is greater than 0.

3) Option A is correct

Null: μd = 0

Alt: μd > 0

4) Given:

n = 24

d' = 1.875

Sd = 4.812

Find test statistic:

$t = \frac{d'}{Sd/\sqrt{n}}$

$= \frac{1.875}{4.812/\sqrt{24}}$

$t = 1.909$

Degree of freedom, df = n - 1 = 24 - 1 = 23

Pvalue $= (t_2_3 > 1.909) = 0.0344$

Pvalue = 0.0344

Significance level = 0.05

5) Since p value is less than significance level, reject null hypothesis H0

Hence, there is strong evidence that, on average, husbands are older than their wives in Cumberland County