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Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.89 hours of personal time per year with a standard deviation of 3.29 hours. The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is ________.

User DerpyNerd
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1 Answer

24 votes
24 votes

Answer:

The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is

contained by the interval (0.54 , 5.18)

Explanation:

Given that:

for women

sample size = n₁ = 16

sample mean
image = 24.75

standard deviation s₁ = 2.84

for men

sample size for men = n₂ = 7

sample mean
image = 21.89

standard deviation s₂ = 3.29

degree of freedom =
image

= 16 + 7 -2

= 21

The critical value for
image


image

The pooled standard deviation can be calculated as follows since the population variances are assumed to be equivalent.


image


image


image


image

The standard error is estimated as follow:


image


image

se = 1.348

Finally, the confidence interval
image


image

User Nandan Singh
by
3.0k points
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