Comparing P value to significance level for test involving difference of proportions
About this video
A veterinarian tests whether a disease affects a larger proportion of male cats (24 of 259) than female cats (14 of 241). Given z = 1.46 and a P-value of about 0.07, the video compares the P-value with alpha = 0.10. Because 0.07 < 0.10, we reject the null hypothesis, which gives evidence that a larger proportion of male cats have the disease.
You'll be able to
- explain what a P-value means in a test for a difference in proportions.
- compare a P-value with a significance level to decide whether to reject H0.
- state the conclusion of a two-proportion test in context.
Key words
- P-value
- The probability of getting data at least as extreme as ours, assuming the null hypothesis is true.
- significance level (alpha)
- The threshold, here 0.10, that the P-value is compared with.
- test statistic
- A number, here z = 1.46, measuring how far the sample result is from what H0 predicts.
- reject the null hypothesis
- Decide the data are too unlikely under H0, which suggests the alternative is true.
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.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.