Question

a random sample of 81 executives (these 81 include both male and female) is drawn for the purpose of estimating the population proportion of females and the mean age of all female executives. The sample contains 33 female executives and for those ladies, the sample mean and standard deviation are 46.5 years and 6.8 years, respectively. We now want to build a confidence interval for the mean age of all female executives.

a.: check that the conditions to build a confidence interval are satisfied

b.: find the margin of error for a 98% confidence interval

c.: find a 98% confidence interval for the mean age of all female executives

d.:interpret the confidence interval

Answer 1

a) Conditions :

i) The sample is a simple random sample

ii) The observations are independent.

iii) The sample data is normally distributed with large sample size. (n>30)

b) The margin of error for a 98% confidence interval is ,

Where , ; The Exvel function is , =TINV(0.02,32)

c) The 98% confidence interval for the mean age of all female executives is ,

d) Interpretation :

There is 98% confidence that the true population mean age of all female executives is is fall within the interval (43.6010,49.3990)