Statistic question

Question

Almost all employees working for financial companies in New York City receive large bonuses at the end of the year. A sample of 63 employees selected from financial companies in New York City showed that they received an average bonus of dollar-sign 50 Number , 000 last year with a standard deviation of dollar-sign 24 Number , 000. Construct a 95 % confidence interval for the average bonus that all employees working for financial companies in New York City received last year.


Round your answers to two decimal places.

to dollars

Answer 1

The best estimate of a population mean is the mean of a sample drawn randomly from that population, in the present case, 50,000 dollars. A confidence interval is this mean value plus or minus the margin of error. The margin of error is equal to the population standard deviation divided by the square root of sample size (in the present case 24,000/sqrt 63, or 3024), multiplied times the confidence coefficient. For a 95% confidence interval, the confidence coefficient is 1.96. Therefore the margin of error is 3024 X 1.96, or 5927. The confidence interval is therefor 50,000 plus or minus 5927, meaning that there is a 95% probability that the true population mean lies between 44,073 and 55,927.