Question

A sample of 100 ages, drawn from a normally distributed population, has a mean of 36 years. The population standard deviation is 4 years. Test the hypothesis that the population mean is 35 years, at = 0.01

Answer 1

$n=100 \\ \bar{x}=36 \\ \sigma= 4 \\ H_0: \mu=35 \\ H_1: \mu ≠35$

Test-statistic:

$Z = \frac{\bar{x} -\mu}{\sigma/ \sqrt{n}} \\ Z= \frac{36-35}{4 / \sqrt{100}} = 2.5 \\ α=0.01$

Two-tailed test.

Reject H₀ if Z≤ -2.575 or Z≥2.575

Conclusion: Since Z= 2.5 < 2.575, accept H₀.

There is enough evidence to conclude that the population mean is 35 years, at α= 0.01.