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:

H

_{0}: p = 0.4

H

_{A}: p ≠ 0.4

## Compute

p^ = 0.35

## Calculate our test statistic z:

z = | 0.35 - 0.4 |

| √0.4(1 - 0.4)/100 |

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 H_{0}

##### 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 H_{0}

##### 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.

H_{1} - 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.

H_{0} - 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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