Question

A random sample of 136 observations produced a sample mean of 29. Find the critical and observed values of z for the following test of hypothesis using a=0.1. The population standard deviation is known to be 5 and the population distribution is normal. H0: mean = 28 versus H1: mean not equal to 28. Round your answers to two decimal places.
zcritical left=

zcritical right =

zobserved =

Answer 1

Given : µ = 28 , σ = 5, n=136 , = 29 , α = 0.1

Step 1) Establish the hypothesi:

H0 : µ = 28 Vs   H1 : µ ≠ 28

Step 2) calculating test statistics.

Population standard deviation σ is known, we use z statistic.

Test statistic

Z =      =       = 2.33

Z observed = 2.33

Step 3) Critical region:

The critical value is based on H1 and α = 0.1.

Since we have two tail test( H1 contains ≠ sign ).

The critical value is α/2 = 0.1/2 = 0.05

That is 5% for left side and 5% for right side of the standard normal table.

We have to find value of z having probability 0.05 for the left side and 0.95 for the right side from the z distribution table.

From standard normal table

Z left    =-1.64   and Z right =1.64

Z Observed =2.33

Step 4)

Conclusion: Observed test statistics lies beyond the critical values, we reject H0 .