Question

# Almost all employees working for financial companies in New York City receive large bonuses at the...

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 _______

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

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