00:01
Okay, so we're told that the population proportion of students ever using, sorry, 18 to 25 year olds ever using cocaine is p equals 0 .1.
00:12
We take a sample of 10 students at a university and find that none have ever used cocaine, so our sample proportion is zero.
00:21
What is the probability of observing no cocaine users in the sample if this probability is true? now we're just going to use so we're looking for the probability that p is less than or equal to zero.
00:38
We're just going to use the fact that p is normally distributed with mean p and standard deviation, although it will, i should say variance, we usually write the variance here in the normal distribution thing, and variance p times 1 minus p over n.
01:04
And so standardizing this is just the same as probability that z is less than or equal to zero minus 0 .1 divided by the square root of 0 .1 times 0 .9 divided by, and this turns out to be the probability that z is less than minus 1 .05, which is 0 .14686.
01:36
Using an alpha of 0 .05 test the null hypothesis the probability of cocaine use is 0 .1.
01:43
So the null hypothesis is going to be that the population proportion is 0 .1.
01:46
So now we're pretending we don't know this fact and we've just got this sample result and we're going to test whether we think this is the case or not.
01:56
Against the alternative hypothesis that it's less than 0 .1...