Find Testing of Mean When population is Normal Variance is Known On Ms. Excel

When population is Normal Variance is Known:

Let's start admit that this is completely unrealistic, that we will find ourselves in the situation to know the population variance, but not the average population. Therefore,  to learn method of hypothesis testing, we have limited practical application. We learn it, just because we will use it to understand hypothesis testing "power" (learning how to calculate the Type II error rate). As usual, let's start with an example.

Example:

A random sample of size 36 is taken from a normal population with a known variance σ² =25
if the mean of the sample is x̅=42.6 ,test the null hypothesis μ=45 against the alternative
hypothesis	μ<45 with α=0.05 (α is the probability of committing Type Ι- error).

For two sided Test:

Formulas:

Z-cal = X̅-μ/(σ/√n) 

Z-tab= = NORMSINV(σ/2)

p-value=  2*(1-NORMSDIST(ABS(Z-cal)))

Now the solution of Example:

When population is Normal Variance is Known for two sided

For One sided Test:

Upper Tail

Z-cal = X̅-μ/(σ/√n) 

Z-tab= = NORMSINV(σ)

p-value= NORMSDIST(ABS(Z-cal))

Now the solution of Example:

When population is Normal Variance is Known for one sided upper tail

Lower Tail

Z-cal = X̅-μ/(σ/√n) 

Z-tab= = NORMSINV(σ)

p-value= NORMSDIST(ABS(Z-cal))

Now the solution of Example:

When population is Normal Variance is Known for one sided lower tail