The ages of the 79 actresses at the time that they won oscars for the best actre

Question

The ages of the 79 actresses at the time that they won oscars for the best actress category have a mean of 35.8 years and a standard deviation of 11.3 years. The ages of the 79 actors at the time that they won Oscars for the category of best actor ahave amean of 43.8 years and a standard deviation of 8.9 years. Assume that the samples are simple random samples.<BR><BR>Construct the 99% confidence interval estimate of the mean age of actresses at the time that they win oscars.<BR><BR>construct the 99% confidence interval estimate of the mean age of actors at the time that they win oscars.<BR><BR>compare the results.

Explanation / Answer

actresses: sample size, n = 79   mean , µ = 35.8 standard deviation, s = 11.3 standard error,e = s / vn = 11.3/v79 = 1.27 at 99% confidence for a two tail distribution, z = 2.58 (from z table) the 99% confidence interval estimate of the mean age of actresses at the time that they win oscars = µ ± (z * e ) =35.8 ± (2.58*1.27) =(32.5234, 39.0766) actors: sample size, n = 79   mean , µ = 43.8 standard deviation, s = 8.9 standard error,e = s / vn = 8.9/v79 = 1.001 at 99% confidence for a two tail distribution, z = 2.58 (from z table) the 99% confidence interval estimate of the mean age of actors at the time that they win oscars = µ ± (z * e ) =43.8 ± (2.58*1.001) =(41.217, 46.383) actors: sample size, n = 79   mean , µ = 43.8 standard deviation, s = 8.9 standard error,e = s / vn = 8.9/v79 = 1.001 at 99% confidence for a two tail distribution, z = 2.58 (from z table) the 99% confidence interval estimate of the mean age of actors at the time that they win oscars = µ ± (z * e ) =43.8 ± (2.58*1.001) =(41.217, 46.383)

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