00:01
So in this question we want to determine if a normal sampling distribution can be used, and we have p is the population proportion, alpha is the significance level, p hat is the sample proportion, and n is the sample size, and if it can be used we will test the claim.
00:48
Now our claim is that p is greater than or equal to 0 .25, we have alpha is 0 .04, and our sample statistics of the p hat is 0 .20, n is 80, and we are going to let q is 1 minus p and q hat is 1 minus p hat.
01:19
Now let's see whether a normal sampling distribution can be used.
01:22
So normal sampling distribution can be used if n p hat is greater than 10 and n q hat is greater than 10.
01:44
Now n p hat is 80 times 0 .2, and 80 times 0 .2 is 16, which is greater than 10, so that's good, and q hat is 80 times 1 minus 0 .2, which is 80 times 0 .8, which is 64.
02:04
This is also greater than 10, so we're happy.
02:08
So it can be used, so the normal distribution can be used, and that means that p hat is normal with the mean of p hat equals p, and the standard deviation of p hat is the square root of p 1 minus p over n.
02:34
Now our null hypothesis is the claim hypothesis that p is at least 0 .25, and our alternate is that p is less than 0 .25, so we're doing a left tail test where the null is the claim hypothesis.
02:57
Now let's remember our sample statistics...