64 randomly selected items were tested. It was found that 56 of the items tested positive.
Test the hypothesis that exactly 80% of the items tested positive at α = 0.01
State the null and alternative hypothesis:
H
0: p = 0.8
H
A: p ≠ 0.8
Compute
p^ = 0.875
Calculate our test statistic z:
z = | 0.875 - 0.8 |
| √0.8(1 - 0.8)/64 |
z = 1.5
Checking our table of z-scores for α = 0.01%, we get:
Z = 2.3263
Our rejection region is Z > 2.3263
Since our test statistic of 1.5 is less than our Z-value of 2.3263, it is not in the rejection region, so we accept H0
You have 2 free calculationss remaining
What is the Answer?
Since our test statistic of 1.5 is less than our Z-value of 2.3263, 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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