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 $48,000 last year with a standard deviation of $16,000. Construct a 95% confidence interval for the average bonus that all employees working for financial companies in New York City received last year.

______ to _______

Answer 1

sample mean, xbar = 48000
sample standard deviation, s = 16000
sample size, n = 63
degrees of freedom, df = n - 1 = 62

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.999

ME = tc * s/sqrt(n)
ME = 1.999 * 16000/sqrt(63)
ME = 4029.605

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (48000 - 1.999 * 16000/sqrt(63) , 48000 + 1.999 * 16000/sqrt(63))
CI = (43970.39 , 52029.61)

CI = (43970 , 52030) nearest dollar

43970 to 52030