Enter x (# of successes) Enter n (sample size) Enter H0 Enter α
p

100 randomly selected items were tested. It was found that 50 of the items tested positive.
Test the hypothesis that exactly 40% of the items tested positive at α = 0.05

H0:  p = 0.4
HA:  p ≠ 0.4

## Compute

 p^  = x n

 p^  = 50 100

p^ = 0.5

## Calculate our test statistic z:

 z  = p^ - p √p(1 - p)/n

 z  = 0.5 - 0.4 √0.4(1 - 0.4)/100

 z  = 0.1 √0.4(0.6)/100

 z  = 0.1 √0.0024

 z  = 0.1 0.0489898

z = 2.0412414523193

## Checking our table of z-scores for α = 0.05%, we get:

Z = 1.6449

Our rejection region is Z > 1.6449

Since our test statistic of 2.0412414523193 is greater than our Z-value of 1.6449, it is in the rejection region, so we reject H0

Since our test statistic of 2.0412414523193 is greater than our Z-value of 1.6449, it is in the rejection region, so we reject H0
##### How does the Hypothesis Testing for a proportion Calculator work?
Free Hypothesis Testing for a proportion Calculator - Performs hypothesis testing using a test statistic for a proportion value.
This calculator has 4 inputs.

### What 2 formulas are used for the Hypothesis Testing for a proportion Calculator?

p^ = x/n
z = (p^ - p)/sqrt(p(1 - p)/n)

For more math formulas, check out our Formula Dossier

### What 6 concepts are covered in the Hypothesis Testing for a proportion Calculator?

alternative hypothesis
opposite of null hypothesis. One of the proposed proposition in the hypothesis test.
H1
hypothesis testing
statistical test using a statement of a possible explanation for some conclusions
hypothesis testing for a proportion
an act in statistics whereby an analyst tests an assumption regarding a population proportion
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
sample size
measures the number of individual samples measured or observations used in a survey or experiment.
test statistic
a number calculated by a statistical test