Hypothesis testing for the mean Calculator

Enter X	Enter n (sample size)	Enter standard deviation	Enter H0	Enter α
			μ =<>

 

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25 randomly selected items were tested. It was found that the average of the sample was 520.
The standard deviation of the items tested is 75.
Test the hypothesis that the mean is exactly 500 at α = 0.02

State the null and alternative hypothesis:

H₀:  μ = 500
H_A:  μ ≠ 500

Calculate our test statistic z:

z  =	X - μ
	σ/√n

z  =	520 - 500
	75/√25

z  =	20
	75/5

z  =	20
	15

z = 1.3333333333333

Determine rejection region:

Since our null hypothesis is H₀:  μ = 500, this is a two tailed test
Checking our table of z-scores for α(left); = 0.01 and α(right); = 0.99, we get:
Z left tail of = -2.3263 and Z right tail of 2.3263
Our rejection region is Z < -2.3263 and Z > 2.3263