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

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
HA:  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

Since our test statistic of 1.3333333333333 is not in the rejection region, we accept (cannot reject) H0





What is the Answer?
Since our test statistic of 1.3333333333333 is not in the rejection region, we accept (cannot reject) H0
How does the Hypothesis testing for the mean Calculator work?
Free Hypothesis testing for the mean Calculator - Performs hypothesis testing on the mean both one-tailed and two-tailed and derives a rejection region and conclusion
This calculator has 5 inputs.

What 1 formula is used for the Hypothesis testing for the mean Calculator?

z = (X - μ)/σ/√n

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Hypothesis testing for the mean Calculator?

alternative hypothesis
opposite of null hypothesis. One of the proposed proposition in the hypothesis test.
H1
conclusion
hypothesis
statistical test using a statement of a possible explanation for some conclusions
hypothesis testing for the mean
an act in statistics whereby an analyst tests an assumption regarding a population mean
mean
A statistical measurement also known as the average
null hypothesis
in a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
H0
test statistic
a number calculated by a statistical test

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