Question

A study of working actors looked at age and gender. One sample of 55 male actors had a mean age of 28 and a standard deviation of 2. The other sample included 55 female actors with a mean age of 27 and a standard deviation of 3. Estimate with 87% confidence the difference between the average ages of working male ( μ 1 ) and female ( μ 2 ) actors.

Answer 1

To estimate the difference in average ages between male and female working actors with 87% confidence, we use the confidence interval formula for two means, considering the given sample sizes, means, and standard deviations.

Step-by-step explanation:

The question asks for an estimate of the difference between the average ages of working male and female actors with 87% confidence.

To calculate this, we use the formula for the confidence interval of the difference between two means: CI = (µ_1 - µ_2) ± (z * √((SD_1^2/n_1) + (SD_2^2/n_2))). With mean ages of 28 and 27, standard deviations of 2 and 3, and samples of 55 for both groups, we need to find the critical z-value for 87% confidence and plug our values into the formula to find the interval.