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Hypothesis Testing for a proportion Calculator

Hypothesis Testing for a proportion Calculator MathCelebrity logo Image to Crop 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

State the null and alternative hypothesis:

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
  0.048989794855664

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

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What is the Answer?

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 hypothesisopposite of null hypothesis. One of the proposed proposition in the hypothesis test.
H1hypothesis testingstatistical test using a statement of a possible explanation for some conclusionshypothesis testing for a proportionan act in statistics whereby an analyst tests an assumption regarding a population proportionnull hypothesisin a statistical test, the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.
H0sample sizemeasures the number of individual samples measured or observations used in a survey or experiment.test statistica number calculated by a statistical test

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