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 ,

H_{0} :
= 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

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