00:01
For this problem to begin, we can note that the manufacturer's claim is that the average is a particular value, 32 miles per gallon.
00:10
Our alternative hypothesis then is simply that the average miles per gallon does not equal 32.
00:18
So this is going to be done as a two -tailed test.
00:22
Now we have a sample of size 64, a sample mean value of 30, a sample standard deviation of 4 miles per gallon, but our population standard deviation is unknown.
00:38
So that means it's going to be appropriate to do this as a two -tailed t -test.
00:43
First thing that i'll do here is determine the critical t -score.
00:48
So the t -statistic, or critical t -value, is going to be the t -score for n -1 degrees of freedom, and a tail proportion of half of the level of significance.
00:59
Level of significance is 0 .01, so we want a tail proportion of 0 .005.
01:06
Now what i'll do here, there are a number of ways to find a critical t -value...