Its a boy genetics labs claim their procedures improve the...

It's a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows: Ho p = 0.50, Ha: p > 0.50 \alpha = 0.01 p-value = 0.025 Reject H0: There is enough evidence to conclude that the lab's procedures improve the chances of a boy being born. Do Not Reject H0: There is enough evidence to conclude that the lab's procedures improve the chances of a boy being born. Do Not Reject H): There is not enough evidence to conclude that the lab's procedures improve the chances of a boy being born. Reject H0: There is not enough evidence to conclude that the lab's procedures improve the chances of a boy being born.

Transcript

00:01 We have been given the results for a test of a single population proportion.

00:05 The null hypothesis is that p, the proportion of births that are a boy, is 0 .5.

00:13 The alternative hypothesis, the claim of this lab, is that actually the proportion in their lab is greater than 0 .5.

00:21 And alpha, level of significance, is 0 .01.

00:25 The p -value is 0 .025.

00:30 What do we say here? okay, so first of all, what are we looking at? so p is the population proportion, the proportion of births from this lab that will be a boy.

00:40 If their procedure doesn't work, if it's just the same as not having the procedure, p would be 0 .5.

00:47 If their procedure does work, p would be greater than 0 .5.

00:52 Alpha is a cutoff point, and it's based on a sampling distribution.

00:58 So according to the central limit theorem, if i take every possible sample of a given size, take all of the sample proportions that are boys, and plot those proportions out, i'll get something approximately normal, as long as the sample size is reasonably large.

01:16 And the mean here is p, 0 .5.

01:20 So if i were to take a sample and i got something that falls here on the sampling distribution, i'd look at that and say, okay, the sample proportion is greater than 0 .5.

01:32 But this wasn't unlikely.

01:35 It's very possible here that the population proportion is 0 .5, i just took a sample that happens to have more boys in it, just by chance.

01:44 And then we would not reject the null hypothesis.

01:48 But if my sample proportion fell down here, i'd look at that and say, okay, that was very unlikely to happen if p is 0 .5.

01:57 Therefore, i think p is higher than 0 .5.

02:00 And then we'll support the lab...