The records of the 30 postal employees at a randomly picked postal station showe

Question

The records of the 30 postal employees at a randomly picked postal station showed that the average time these employees had worked for the postal service was
x = 8 years and that there was a sample standard deviation of s=5.

You may assume that the population’s times: x is normally distributed.

a. Compute a 99% confidence interval for the mean time the population of the U. S. postal service employees have spent with the postal service.

b. Give the margin of error of your confidence interval.

c. Explain to someone who might not know statistics what the confidence level means.

Explanation / Answer

A)To compute the 99% Confidence Interval (C.I.) when the is unknown, we use the formula
%CI = Xbar ± t* x (s/n) with Df = n-1

Xbar = 8, s = 5, n=30, df=29

t* can be found in the t-tables where 99% and df=29 cross (t*=2.756)

99%CI = 8 ± 2.576 x (5/30) = 8 ± 2.352 [5.648 - 10.352]

B)Margin of Error = t* x (s/n) = 2.352

C)The confidence level tells us how often we expect to have the true parameter (in this case - mean time working in the postal service) within our confidence interval if we were to take random sample. In this problem, we are confident that if we take another random sample, we have a 99% chance of obtaining a confidence interval that contains the true population mean time that a worker has been in the postal service.

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