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= (41.8-45)/(6/ √(25) ) = (-3.2)/(6/5) = (-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.