00:01
Okay, so we're told here that a newspaper collected a sample of 500 voters and estimated the support to be 52 % for the certain person, okay? and the campaign manager had claimed, this is their alternative hypothesis, their claim, that p was greater than 0 .5, meaning that more than half of people supported the person.
00:31
Okay, however, the sticker is that the p value for this test was 0 .19.
00:39
Okay? so, the interpretation of this p value is that if the null hypothesis was true, which is that p is equal to 0 .5, okay? that's the null hypothesis.
01:04
So if 50 % supported the candidate, okay? then the probability of getting what we did is 0 .19.
01:23
So it's that first interpretation like part a.
01:28
Okay, that is the right thing.
01:30
It doesn't mean that 95 % of samples will show a certain thing.
01:34
It doesn't mean that the success -failure thing is not met because there are greater than 10 successes and failures, so that part is totally met.
01:45
And it is not convincing evidence because the p value is large it's greater than our alpha of 0 .05 okay so if we use okay so if for number 6 we have some hypotheses okay the null hypothesis being that the proportion is equal to 0 .3 and the alternative being that the proportion is not equal to 0 .3 we find a random sample of 50 observations where p hat is equal to .36, and we want to know what is the standard error.
02:31
So the standard error should be the square root of p times 1 minus p over n.
02:40
And usually you should use the p value from the null hypothesis, not the p value from the sample to do that.
02:50
So that's going to be the square root of 0 .3 times 0 .7 over 50, okay, which should be 0 .0648...