A survey of 22 randomly sampled judges employed by the state of Florida found th

Question

A survey of 22 randomly sampled judges employed by the state of Florida found that they earned an average wage (including benefits) of $61.00 per hour. The sample standard deviation was $5.66 per hour. (Use tDistribution Table.) a. What is the best estimate of the population mean? Estimated population mean b. Develop a 98% confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.) Confidence interval for the population mean wage is an etwee c. How large a sample is needed to assess the population mean with an allowable error of $1.00 at 95% confidence? (Round up your answer to the next whole number.) ample size

Explanation / Answer

a)

Estimated popualtion mean = 61.00

b)

CI for 98%

n = 22

mean = 61

t-value of 98% CI = 2.5176

std. dev. = 5.66

SE = std.dev./sqrt(n) = 1.20672

ME = t*SE = 3.03809

Lower Limit = Mean - ME = 57.96191

Upper Limit = Mean + ME = 64.03809

98% CI (57.9619 , 64.0381 )

c)

Given CI Level = 95%

Margin of Error(ME) = 1

std. dev. = 5.66

t-value of 95% CI = 2.0796

n = (z*sigma/ME)^2 = 139

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