A random sample of 27 people employed by the Florida state authority established

Question

A random sample of 27 people employed by the Florida state authority established they earned an average wage (including benefits) of dollar 57.00 per hour. The sample standard deviation was dollar 5.81 per hour. (Use Z Distribution Table) a. What is the best estimate of the population mean? Estimated population mean dollar 57 Develop a 99 percentage 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 between and

Explanation / Answer

Solution:

We are given

Sample size = n = 27

Mean = 57

Standard deviation = 5.81

Confidence level = 99% = 0.99

Significance level = 1 – 0.99 = 0.01

The confidence interval is given as below:

Confidence Interval Estimate for the Mean

Data

Standard Deviation

5.81

Sample Mean

57

Sample Size

27

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

1.1181

Z Value

-2.5758

Interval Half Width

2.8801

Confidence Interval

Interval Lower Limit

54.12

Interval Upper Limit

59.88

Confidence Interval Estimate for the Mean

Data

Standard Deviation

5.81

Sample Mean

57

Sample Size

27

Confidence Level

99%

Intermediate Calculations

Standard Error of the Mean

1.1181

Z Value

-2.5758

Interval Half Width

2.8801

Confidence Interval

Interval Lower Limit

54.12

Interval Upper Limit

59.88

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