Question

A random sample of 115 observations produced a sample mean of 32. 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 6 and the population distribution is normal.

H0: μ=28 versus H1: μ>28.

Round your answers to two decimal places.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 28

H_a : > 28

= 32

= 28

= 6

n = 115

Test statistic = z

= ( - ) / / n

= (32 - 28) / 6 / 115

= 7.15

Test statistic = 7.15

Observed value of z = 7.15

= 0.025

Z_0.025 = 1.96

Critical value = 1.96