Question

A random sample of 100 postal employees found that the average time these employees had worked for the postal service was x(bar) = 7 years, with standard deviation s = 2 years. Assume the distribution of the time the population of employees has worked for the postal service is approximately normal, with mean μ. Are these data evidence that μ has changed from the value of 7.5 years of 20 years ago? Carry a test of significance at 1% and 5% levels.

Answer 1

n = 100

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.
Now, the value of test static can be found out by following formula:

For . Since , we fail to reject the null hypothesis



The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized mean value of 30 on either side.
Now, the value of test static can be found out by following formula:

For . Since , we reject the null hypothesis in favor of the alternative hypothesis .
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