According to a survey, working men reported doing 64.9 minutes of household chores a day, while working women reported tackling 80 minutes daily. But when examined more closely, millennial men reported doing just as many household chores as the average working women, 80 minutes, compared to an average of 58 minutes among both boomer men and Gen Xers. The information that follows is adapted from these data and is based on random samples of 1096 men and 785 women.
Mean | Standard Deviation | n | |
---|---|---|---|
All Women | 80 | 10.4 | 785 |
All Men | 64.9 | 15.5 | 1,096 |
Millennials | 80 | 9.2 | 345 |
Boomers | 58 | 13.9 | 455 |
Xers | 58 | 10.5 | 296 |
(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
a) For men, sample mean , = 64.9
n = 785 and sample standard deviation, s = 15.5
Degrees of freedom = n -1 = 784
For df = 784 and 95% confidence level , t(critical) = 1.96
The confidence interval is = t * s / n
= 64.9 1.084
= (63.8 , 67.0)
Answer : 63.8 minutes to 67 minutes.
b) For women, sample mean , = 80
n = 1096 and sample standard deviation, s = 10.4
Degrees of freedom = n -1 = 1095
For df = 1095 and 95% confidence level , t(critical) = 1.96
The confidence interval is = t * s / n
= 80 0.616
= (79.4 , 80.6)
Answer : 79.4 minutes to 80.6 minutes.
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