00:01
For this problem, to begin, in part 1 we're asked to state the null and alternative hypotheses.
00:06
Specifically, we know that we are testing to see if students enrolled in the gifted program have a higher absenteeism rate.
00:13
So our null hypothesis is going to be that the mean number of days, or the mean absenteeism rate for the gifted students, is equal to that of the general population, which is 7 days per year, while the alternative hypothesis will be that the mean is greater, so mu is greater than 7.
00:38
So we can see that this is a right -tailed test.
00:41
For the second part of the problem, for determining whether the z -test or t -test should be used, we have a pretty small sample, only 17 students, and we also do not know the population standard deviation, so we would use a t -test, because of, as i said, population standard deviation is unknown.
01:14
Then, for finding the critical value, since this is a right -tailed t -test, the critical t -value is going to be the positive t statistic for n -1 degrees of freedom, so that's 16 degrees of freedom here, and a right -tailed proportion of 0 .01.
01:32
Now i'll find that using my table of values over here, 0 .01 in one tail, 16 degrees of freedom, we can see that the critical value is 2 .583...