Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 20 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 20.5 hours of personal time per year with a standard deviation of 2.75
Hours. The pooled estimate of the variance is
A) 264.6715
B) 2.790
C) 7.785
D) 12.998
E) None of the above.

Question

Quizplus · Accepted Answer

To find the pooled estimate of the variance, use the formula:

s^2pooled = [(n1-1)s1^2 + (n2-1)s2^2] / [n1 + n2 - 2]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the given values:

s1 = 2.84, n1 = 16
s2 = 2.75, n2 = 20

s^2pooled = [(16-1)(2.84)^2 + (20-1)(2.75)^2] / [16+20-2]
s^2pooled = (15*8.0656 + 19*7.5625) / 34
s^2pooled = 265.0624 / 34
s^2pooled = 7.788

Therefore, the answer is C) 7.785 (rounded to three decimal places).

Data Were Collected on Annual Personal Time (In Hours) Taken