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## AP®︎/College Statistics

### Unit 10: Lesson 9

Testing for the difference of two population proportions- Hypothesis test for difference in proportions
- Constructing hypotheses for two proportions
- Writing hypotheses for testing the difference of proportions
- Hypothesis test for difference in proportions example
- Test statistic in a two-sample z test for the difference of proportions
- P-value in a two-sample z test for the difference of proportions
- Comparing P value to significance level for test involving difference of proportions
- Confidence interval for hypothesis test for difference in proportions
- Making conclusions about the difference of proportions

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# Comparing P value to significance level for test involving difference of proportions

AP.STATS:

DAT‑3 (EU)

, DAT‑3.C (LO)

, DAT‑3.C.1 (EK)

, DAT‑3.D (LO)

, DAT‑3.D.1 (EK)

, DAT‑3.D.2 (EK)

Comparing P value to significance level for test involving difference of proportions.

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## Video transcript

- [Instructor] A veterinarian
is studying a certain disease that seems to be affecting male
cats more than female cats. They obtain a random sample
of records from 500 cats. They find 24 of the 259
male cats have the disease while 14 of 241 female
cats have the disease. The veterinarian uses these results to test their null hypothesis that the true proportion is
the same amongst the male and female cats versus the alternative hypothesis that the proportion of
males who get the disease is actually higher than
the proportion of females. The test statistic was z is equal to 1.46 and the P-value was approximately 0.07. That's useful. They've done a lot of work for us. Assume that all conditions
for inference were met. At the alpha equals 0.10
level of significance, is there sufficient evidence to conclude that a larger proportion of
male cats have the disease? So pause this video and
see if you can answer that. All right, so remember what we
do with a significance test. We assume our null hypothesis, and then given, and then with that assumption, we look at our data and we calculate a P-value. We say, hey, what is the probability of
getting the data that we did assuming our null hypothesis is true? And if that is lower than
our significance level, then we reject the null hypothesis. We say, hey, assuming the null hypothesis, we got a pretty unlikely event. We reject it. Which would suggest the alternative. And so here our P-value is 0.07, which is indeed less than our alpha, which is less than our significance level. This thing right over here is 0.10. And so because of that, we would reject the null hypothesis. Reject null hypothesis. Which would, which is, we could say there is
sufficient evidence to conclude that a larger proportion of
male cats have the disease. We could say suggests the
alternative hypothesis. And so on Khan Academy there's some multiple
choice questions like this, and so the choice that you would pick might be something like, because our P-value is less
than our significance level, we would reject the null hypothesis, and that would suggest the alternative.