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

100 randomly selected items were tested. It was found that 35 of the items tested positive.
Test the hypothesis that exactly 40% of the items tested positive at α = 0.05

State the null and alternative hypothesis:

H0:  p = 0.4
HA:  p ≠ 0.4

Compute

p^  =  x
  n

p^  =  35
  100

p^ = 0.35

Calculate our test statistic z:

z  =  p^ - p
  p(1 - p)/n

z  =  0.35 - 0.4
  0.4(1 - 0.4)/100

z  =  -0.05
  0.4(0.6)/100

z  =  -0.05
  0.0024

z  =  -0.05
  0.048989794855664

z = -1.0206207261597

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 -1.0206207261597 is less than our Z-value of 1.6449, it is not in the rejection region, so we accept H0





What is the Answer?
Since our test statistic of -1.0206207261597 is less than our Z-value of 1.6449, it is not in the rejection region, so we accept 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

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