00:01
Okay, so we want to test whether there is a difference in the daily water usage after and before the campaign.
00:10
So we're going to compute the difference d as the before value minus the after value, and our null hypothesis is going to be that the population mean difference between the before value minus the after value for an individual person is equal to zero, and the alternative hypothesis is going to be that it's different from zero.
00:31
For part b, we're asked to state the design assumptions and requirements.
00:37
So we need all the households to be independent, and we need the before and after measures to be from the same household, and we need the population mean of the differences to be normally distributed.
01:08
So those are our assumptions.
01:12
Part c says state the decision rule.
01:14
We will reject the null hypothesis if our test statistic t is bigger than, so because we've got a two -tailed test, and we're asked to conduct it at the 5 % level, we're cutting off the top and bottom 2 .5%, and so the t values bounding these regions are t cutting off the top 2 .5 % of the t distribution with n minus one, which is seven degrees of freedom, and then the lower value will just be minus that, and if you look up that value in your tables, it's 2 .365.
02:03
So we reject if our test statistic is bigger than plus 2 .365 or less than minus 2 .365, because then we're in these critical regions that i've drawn here.
02:13
Part d says to calculate the value of the test statistic and make a decision.
02:17
So the value of the test statistic is just given by the mean of the differences, divided by the standard deviation of the differences over the square root of the sample size...