00:01
For this problem, to begin, we know that our claim is that this hybrid model gets an average of 60 miles per gallon.
00:08
So that's going to be our null hypothesis.
00:12
The alternate hypothesis is the car enthusiast's suspicion that the average is lower, that mu is then less than 60.
00:23
We have a sample mean value equal to 58 .2, a sample size of 12 cars, and a sample standard deviation of 4 miles per gallon.
00:36
Now i'll note that because we have a sample size that is pretty small and an unknown population standard deviation, we need to assume that the population is normally distributed in order for us to be able to do our hypothesis test here.
00:55
So we'll just put that down there, sort of acknowledge that that is a necessary assumption in this case.
01:01
So we are doing a left -tailed hypothesis test for an unknown population standard deviation.
01:07
So our decision rule here is going to be that we will reject the null hypothesis if our observed t -statistic is less than the negative t -value for n -1 degrees of freedom, so that's 11 degrees of freedom, and a one -tailed proportion of 0 .05...