Question
In: Statistics and Probability
A study of working actors looked at age and gender. One sample of 55 male actors...
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 <
Solutions
Expert Solution
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)
----------------------------------------------------------------------The End ------------------------------------------------------------------------
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orchestra answered 1 year agoRelated Solutions
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