Question

A random sample of 102 observations produced a sample mean of 30. Find the critical and observed values of z for the following test of hypothesis using α=0.01. The population standard deviation is known to be 8 and the population distribution is normal.

H0: μ=28 versus H1: μ≠28.

Round your answers to two decimal places.

z_{critical left} =

z_{critical right} =

z_observed =

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 28

Ha : 28

α = 0.01

z critical left = zα = -2.33

z critical right = zα = 2.33

Test statistic = z observed =

= ( - ) / / n

= (30 - 28) / 8 / 102

z observed =  2.52