Comparing P value to significance level for test involving difference of proportions | Khan Academy

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 the significance test. We assume our null hypothesis, and then given 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?" If that is lower than our significance level, then we reject the null hypothesis because we say, "Hey, assuming the null hypothesis, we got a pretty unlikely event."

We reject it, which would suggest the alternative. 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, 0.10. Because of that, we would reject the null hypothesis.

Rejecting the null hypothesis would suggest that there is sufficient evidence to conclude that a larger proportion of male cats have the disease. So we could say it suggests the alternative hypothesis.

On Khan Academy, there are some multiple choice questions like this, and 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.