Question

A study of working actors looked at age and gender. One sample of 55 male actors had a mean age of 25 and a standard deviation of 4. The other sample included 55 female actors with a mean age of 28 and a standard deviation of 2. Estimate with 91% confidence the difference between the average ages of working male (μ1μ1) and female (μ2μ2) actors. Round answers to the nearest hundredth.
< μ1−μ2μ1-μ2 <

Answer 1

ANSWER:

Given that,

A study of working actors looked at age and gender. One sample of 55 male actors had a mean age of 25 and a standard deviation of 4. The other sample included 55 female actors with a mean age of 28 and a standard deviation of 2.

= 55	= 55
= 25	= 28
= 4	= 2

Estimate with 91% confidence the difference between the average ages of working male (μ1μ1) and female (μ2μ2) actors.

Degree of freedom = df = +-2 = 55+55-2 = 108

c = 91% = 91/100 = 0.91

= 1-c =1-0.91 = 0.09

/2 = 0.09/2 = 0.045

Critical value = = = 1.71074

91% CI = (-) *sqrt(/+/)

91% CI = (25-28) 1.71074*sqrt(4^2/55+2^2/55)

91% CI = -3 1.031615035

-3-1.031615035<  - < -3+1.031615035

-4.031 <  - < -1.968

-4.031 <  - < -1.968 (Rounded to three decimal places)

91% confidence interval : (-4.031 , -1.968)

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