Question

A random sample of 119 observations produced a sample mean of 31. 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 9 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

= 0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

zcritical left = -2.58

zcritical right = 2.58

Test statistic = z =

= ( - ) / / n

= (31- 28) / 9 / 119

Test statistic = z = 3.64