00:01
For this exercise, we are asked to test the null hypothesis that the mean impurity concentration in pills is 3 % versus the alternative hypothesis that the mean is greater than 3%.
00:13
And we are asked to test at a significance level of alpha equals .05.
00:20
To do so, we have a sample of 25, which was randomly selected for these pills, and the sample mean was 3 .4 % impurities, with a sample standard.
00:32
Standard deviation of 0 .3.
00:36
Now for part a we are asked to calculate the test statistic.
00:41
Since we don't have the population standard deviation, and we are relying on sample standard deviation, the test statistic is based on the t distribution, and it's equal to the sample mean minus the null hypothesized mean, divided by the sample standard deviation over the square root of the sample size.
01:15
And this comes out to 6 .67, 6 .67, approximately.
01:23
And for part b, we are asked to provide the critical value...