Question

A high school counselor wishes to test the theory that the average age of the dropouts...

A high school counselor wishes to test the theory that the average age of the dropouts in his school district is 16.3 years. He samples 32 recent dropouts and finds that their mean age is 16.9 years. At a =0.01, is the theory correct? The standard deviation of the population is 0.3. Construct a corresponding confidence interval for the population parameter.
Math   Statistics-And-Probability   
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Answer #1

Null Hypothesis, H0: Average Age = 16.3

Alternate Hypothesis, Ha: Average Age 16.3

At , the critical z-value corresponding to is 2.5758 (Can be looked up from standard z-table or found using Excel formula NORM.S.INV(0.995)

Test Statistic =

Since the test statistic > critical z-value, we can reject the theory (null hypothesis).

Confidence interval for population mean is given as

The Confidence interval for population mean is [16.1635, 16.4365]

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