Question

Consider H0: μ = 45 versus H1: μ < 45. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025 and the population is known to be normally distributed with σ = 6.

Answer 1

Given
$H0: \ \mu=45 \\ \\ H1: \ \mu\ \textless \ 45$
This is a one-tailed test.

$z= \frac{41.8-45}{6/ \sqrt{25} } = \frac{-3.2}{6/5} = \frac{-3.2}{1.2} =-2.6667$

$P(z\ \textless \ -2.6667)=0.00383$

Since the p-value of the sample statistic (0.00383) is less that the significant level (0.025), we reject the null hypothesis.