You wish to test the claim that 24 at a level of significanc

You wish to test the claim that 24 at a level of significance of = 0.01 and are given sample statistics n = 40, = 25.8. Assume the population standard deviation is 4.3. Compute the value of the standardized test statistic. Round your answer to two decimal places.

Solution

First set up null and alternate hypothesis as

H0: mu = 24

Ha: mu <=24

Left tailed test for mean

n = sample size = 40

and x bar =25.8

Hence mean diffrence = 25.8-24 = 1.8

Std error = std dev/rtn = 4.3/rt 40 = 0.680

As sample size >30 and population std deviation is known, z test can be used

Z statistic = mean diff./std error = 1.8/0.68

= 2.65