Suppose we have a Proportion Test, testing the % of iPhone users in a class.The null hypothesis H0 is: p = 0.5.We take a sample of 10, and the observed value is 7.What is the test statistic?
Question
Suppose we have a Proportion Test, testing the % of iPhone users in a class.The null hypothesis H0 is: p = 0.5.We take a sample of 10, and the observed value is 7.What is the test statistic?
Solution
The test statistic for a proportion test can be calculated using the formula:
Z = (p̂ - p0) / sqrt((p0 * (1 - p0)) / n)
where:
- p̂ is the observed proportion in your sample,
- p0 is the proportion stated in your null hypothesis,
- n is the size of your sample.
In this case:
- p̂ = 7/10 = 0.7 (because 7 out of 10 students are iPhone users),
- p0 = 0.5 (from the null hypothesis),
- n = 10 (the size of the sample).
Substituting these values into the formula gives:
Z = (0.7 - 0.5) / sqrt((0.5 * (1 - 0.5)) / 10) Z = 0.2 / sqrt(0.025) Z = 0.2 / 0.158 Z = 1.27
So, the test statistic (Z) is approximately 1.27.
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