Question

Question 1 (1 point)

Do women tend to spend more time on housework than men? If so, how much more? A survey asked, "On average, how many hours a week do you personally spend on housework, not including childcare and leisure time activities?" The following are the responses (in hours) of 12 women and 15 men.

Women: 16, 12, 10, 14, 15, 6, 11, 9, 12, 7, 12, 15

Men: 5, 3, 8, 11, 4, 3, 6, 2, 8, 12, 9, 9, 3, 11, 10

(a) What is a 95% confidence interval for the difference between the mean time on housework for women and the mean time on housework for men?

Question 1 options:

	(2.48, 6.82)
	(1.10, 8.20)
	(2.03, 7.27)
	(2.33, 6.97)

Question 2 (1 point)

Do women tend to spend more time on housework than men? If so, how much more? A survey asked, "On average, how many hours a week do you personally spend on housework, not including childcare and leisure time activities?" The following are the responses (in hours) of 12 women and 15 men.

Women: 16, 12, 10, 14, 15, 6, 11, 9, 12, 7, 12, 15

Men: 5, 3, 8, 11, 4, 3, 6, 2, 8, 12, 9, 9, 3, 11, 10

Test, at significance level 0.05, that there is a difference between the mean time on housework for women and the mean time on housework for men.

This is a

Question 2 options:

	One-sample t test
	One-sample z test
	Two-sample t test
	Paired two-sample t test

Question 3 (1 point)

Do women tend to spend more time on housework than men? If so, how much more? A survey asked, "On average, how many hours a week do you personally spend on housework, not including childcare and leisure time activities?" The following are the responses (in hours) of 12 women and 15 men.

Women: 16, 12, 10, 14, 15, 6, 11, 9, 12, 7, 12, 15

Men: 5, 3, 8, 11, 4, 3, 6, 2, 8, 12, 9, 9, 3, 11, 10

Test, at significance level 0.05, that there is a difference between the mean time on housework for women and the mean time on housework for men.

The value of the test statistic is

Question 3 options:

	2.68
	2.94
	3.15
	3.66

Question 4 (1 point)

Do women tend to spend more time on housework than men? If so, how much more? A survey asked, "On average, how many hours a week do you personally spend on housework, not including childcare and leisure time activities?" The following are the responses (in hours) of 12 women and 15 men.

Women: 16, 12, 10, 14, 15, 6, 11, 9, 12, 7, 12, 15

Men: 5, 3, 8, 11, 4, 3, 6, 2, 8, 12, 9, 9, 3, 11, 10

Test, at significance level 0.05, that there is a difference between the mean time on housework for women and the mean time on housework for men.

The p-value of the test is

Question 4 options:

	Less than 0.01
	Between 0.01 and 0.05
	Between 0.05 and 0.10
	Greater than 0.10

Question 5 (1 point)

Do women tend to spend more time on housework than men? If so, how much more? A survey asked, "On average, how many hours a week do you personally spend on housework, not including childcare and leisure time activities?" The following are the responses (in hours) of 12 women and 15 men.

Women: 16, 12, 10, 14, 15, 6, 11, 9, 12, 7, 12, 15

Men: 5, 3, 8, 11, 4, 3, 6, 2, 8, 12, 9, 9, 3, 11, 10

Test, at significance level 0.05, that there is a difference between the mean time on housework for women and the mean time on housework for men.

What is the conclusion of the test?

Question 5 options:

	The data provide sufficient evidence that there is a difference between the mean time on housework for women and the mean time on housework for men.
	The data do not provide sufficient evidence that there is a difference between the mean time on housework for women and the mean time on housework for men.
	The data provide sufficient evidence that there is no difference between the mean time on housework for women and the mean time on housework for men.
	The data do not provide sufficient evidence that there is no difference between the mean time on housework for women and the mean time on housework for men.

Answer 1

Q1:

For Women :

∑x = 139

∑x² = 1721

n1 = 12

Mean , x̅1 = Ʃx/n = 139/12 = 11.5833

Standard deviation, s2 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(1721-(139)²/12)/(12-1)] = 3.1754

For Men :

∑x = 104

∑x² = 884

n2 = 15

Mean , x̅2 = Ʃx/n = 104/15 = 6.9333

Standard deviation, s2 = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(884-(104)²/15)/(15-1)] = 3.4115

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 24.3682 = 24

95% Confidence interval for the difference :

At α = 0.05 and df = 24, two tailed critical value, t_c = T.INV.2T(0.05, 24) = 2.064

Lower Bound = (x̅1 - x̅2) - t_c*√(s1²/n1 +s2²/n2) = (11.5833 - 6.9333) - 2.064*√(3.1754²/12 + 3.4115²/15) = 2.03

Upper Bound = (x̅1 - x̅2) + t_c*√(s1²/n1 +s2²/n2) = (11.5833 - 6.9333) + 2.064*√(3.1754²/12 + 3.4115²/15) = 7.27

Answer: (2.03, 7.27)

-----

Q2: Answer: This is a two-sample t test.

-----

Q3:

Test statistic:  

t = (x̅1 - x̅2)/√(s1²/n1 + s2²/n2) = (11.5833 - 6.9333)/√(3.1754²/12 + 3.4115²/15) = 3.66

----

Q4: Right tailed p-value = T.DIST.RT(3.6577, 24) = 0.0006

Answer: p-value is less than 0.01

---

Q5: Conclusion :

The data provide sufficient evidence that there is a difference between the mean time on housework for women and the mean time on housework for men.