Test the hypothesis using p-value approach assuming the...

Transcript

00:01 We want to perform a hypothesis test.

00:03 Now, the null hypothesis is the population proportion is 0 .6.

00:09 Alternative, it is less than 0 .6.

00:12 Our sample size is 250.

00:15 Out of these, we saw 124 successes.

00:19 Members of the sample that met for criteria.

00:22 That's a sample proportion of 124 out of 250 or 0 .496.

00:30 To perform a test, you assume the null hypothesis is true, so pretend p is 0 .6, and to look at the sampling distribution you would expect to see.

00:40 If we took every sample of size 250, took the sample proportions and plotted them out, we'd get something approximately normal.

00:49 This is a normal approximation to the binomial.

00:53 P hat follows normal curve, mean p, standard deviation, root p1 minus p over n.

01:00 These are the mean and standard deviation of the binomial, except we divided everything by n, because we're not looking at the number of successes, we're looking at the proportion.

01:10 Okay, so this is what i expect.

01:13 The big question is, where does my sample fall on this curve? maybe it's here.

01:17 Less than 0 .6, but it wasn't that unlikely.

01:20 I wouldn't be surprised to see this if the null hypothesis is true.

01:24 The same way that when you flip a coin 10 times, you expect 5 tails.

01:27 You wouldn't be shocked if you got 6.

01:30 Or maybe my sample is out here.

01:33 Then i would say, if the null hypothesis is true, this is really unlikely.

01:38 Therefore, i don't think it's true.

01:40 Alpha, the level of significance, is the cutoff point where something becomes so unlikely that i reject the null hypothesis...

Question

Test the hypothesis using p-value approach assuming the requirements have been met. H0 : p = 0.6 H1 : p < 0.6 n=250, x=124, ? = 0.01

Question

Test the hypothesis using p-value approach assuming the requirements have been met. H0 : p = 0.6 H1 : p < 0.6 n=250, x=124, ? = 0.01

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