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 = 0.4HA: 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 = 1.6449Our 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
You have 2 free calculationss remaining
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.
This calculator has 4 inputs.
What 2 formulas are used for the Hypothesis Testing for a proportion Calculator?
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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