00:01
So you have 737 respondents and they had a p -hat of 92%, which was, if you take 92 % of 0 .92 times 737, that comes out to be basically about 678 out of 737.
00:23
And when you do get that p -value, i did a one proportion z -test and entered that in, and you do get that the test statistic is 10 .65, which is greater than a critical value to have the all 0 .01 is our significance level and 0 .01 in the upper tail is approximately a critical value of 2 .33.
00:55
And so we would reject the null.
00:58
And since they are voluntary response, the results are not necessarily valid at this level.
01:06
So i would agree with that.
01:10
So if these are volunteers, we would have to be very careful about using that information.
01:17
But you would have evidence to reject the null if these had been random people and their voluntary response is a problem.
01:27
Now, the next question says that in a sample of 36 homes are taken, the sample mean is found to be 1 .97 hours with a sample standard deviation that is found to be 0 .1 hours.
01:43
And you want to use a 0 .05 significance level and to find out whether i guess there is a difference.
01:51
And so if we add a 0 .05, that means we could find a 95 % confidence interval.
02:01
And it says using its significance level, the test statistic would be again a t -value.
02:09
So i'm going to enter that data in.
02:11
And we think that it is less than 2 hours.
02:16
So the mean would be that the mean is greater than or equal to 2 and alternately that the mean is less than 2 hours.
02:24
So that is a t -test.
02:27
And we have statistics.
02:29
And we would put the mean as 2, the x -bar as 1 .97, the sample standard deviation of 0 .1, and the sample size of 36.
02:38
And again, it is a less than test.
02:40
And i do get that the t -value is a negative 1 .8.
02:43
And the p -value for this is equal to 0 .040.
02:50
And that is less than that 0 .05.
02:53
So you would have evidence to reject the null.
02:57
So you would have evidence to reject the null because the test statistic is less than the critical value.
03:08
And the critical value, if you have 0 .05 here, the critical value is actually not that value you have...