Question

A random sample of 105 observations produced a sample mean of 33. Find the critical and observed values of z for the following test of hypothesis using α=0.025. The population standard deviation is known to be 9 and the population distribution is normal.

H0: μ=28 versus H1: μ>28.

Round your answers to two decimal places.

z_critical =

z_observed =

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H0 :   = 28

Ha : > 28

α = 0.025.

P(z > z ) = 0.025

= 1 - P(Z < z) = 0.025  

= P(Z < z) = 1 - 0.025

= P(Z < z ) = 0.975

= P(Z < 1.96 ) = 0.975  

z > 1.96

Test statistic = z =

= ( - ) / / n

= (33 - 28) / 9 / 105

Test statistic = z = 5.69