Arandom sample of size 25 from a normal population has the mean = 47.5 and the standard deviation s = 8.4. does this information tend to support or refuse the claim that the mean of the population is = 42.1

The information tends to refuse the claim that the mean of the population is equal to 42.1

Information from the sample:

sample size    n  = 25

Sample mean    x  = 47.5

Sample standard deviation   s  =  8.4

Normal Population and population mean  μ  = 42.1

Hypothesis Test:

A Hypothesis Test will be developed to see if 47.5 is an indication of the

a different μ, therefore.

Null Hypothesis                               H₀                 x  = μ

Alternative Hypothesis                   Hₐ                  x  ≠ μ

We choose a confidence Interval of 95 % then a significance level is

α = 5 %      α = 0,05    α  = 0.025

z critical   z(c) for  α = 0.025  is from   z- table      z(c) = 1.96

Choosing the two tail-test we try to give more change for accepting H₀ since the rejection region is small ( or the z(c) is bigger)

To calculate z(s)

z(s) =  ( x  -  μ ) / s/√n

z(s) =   47.5  - 42.1 )/8.4/√25

z(s) =  5.4 * 5 / 8.4

z(s) = 3.21

Comparing z(c)  and z(s)

z(s) > z(c)

Then z(c) is in the rejection region we reject H₀.