Question

A sample of 200 people of age 21 with a population standard deviation of 5. Test the hypothesis that the population mean is 18.9 at à,=0.05.

Answer 1

Null and alternative hypothesis:

$H_0:\mu=18.9$

$H_1:\mu\neq18.9$

Test statistic:

Sample size is greater than 200, so z-test is appropriate as test statistic to conduct hypothesis testing.

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{21-18.9}{\frac{5}{\sqrt{200}}}=5.94$

Critical Value:

z-test critical value at 95% confidence interval = 1.96

Statistical Decision:

z-score is greater than critical value (5.94 > 1.96), so the null hypothesis is rejected in favor of the alternative hypothesis.

Conclusion:

It can conclude that the population mean is not equal to 18.9.