Question

According to a survey, working men reported doing 62.5 minutes of household chores a day, while working women reported tackling 76 minutes daily. But when examined more closely, millennial men reported doing just as many household chores as the average working women, 76 minutes,compared to an average of 57 minutes among both boomer men and Gen Xers. The information that follows is adapted from these data and is based on random samples of 1156 men and 785 women.

	Mean	Standard Deviation	n
All Women	76	10.4	785
All Men	62.5	14.6	1,156
Millennials	76	9.2	335
Boomers	57	13.9	485
Xers	57	10.5	336

(a)

Construct a 95% confidence interval for the average time all men spend doing household chores. (Round your answers to one decimal place.)

( ) minutes to ( ) minutes

(b)

Construct a 95% confidence interval for the average time women spend doing household chores. (Round your answers to one decimal place.)

( )minutes to ( ) minutes

Answer 1

a) Let x be a random variable that denote the number of minutes a working man do household chores a day.

Given, =62.5

sample standard deviation s₁ =14.6

n₁=1156  

Level of significance =0.05

degree of freedom =n₁-1 = (1156-1)=1155

Since sample standard deviation is given therefore we use t-statistic .

therefore 95% confidence interval is =

= (62.5 - t_0.025,1155 14.6/34 , 62.5 + t_0.025,1155 14.6/34)

= (61.657 , 63.343)

Since 95% confidence interval for the average time all men spend doing household chores is (61.7 )minutes to (63.3) minutes.

b)

Let y be a random variable that denote the number of minutes a working woman do household chores a day.

Given, =76

sample standard deviation s₂ =10.4

n₂=785

Level of significance =0.05

degree of freedom =n₂-1 = (785-1)=784

Since sample standard deviation is given therefore we use t-statistic .

therefore 95% confidence interval is =

= (76 - t_0.025,784 10.4/28.02 , 76 + t_0.025,784​​​​​​​ 10.4/28.02)

= (75.271 , 76.729)

Ans :- Since 95% confidence interval for the average time women spend doing household chores is (75.3 )minutes to (76.7) minutes.