00:01
So your first question, you wanted to determine a 99 % confidence interval for the mean gas mileage for that vehicle.
00:07
Now, we were told that this is what they believe it is, and this is what the population standard deviation is.
00:13
Therefore, we will be finding a z interval.
00:17
And so we can see that we take the sample that we got in miles per gallon for those 43 vehicles, plus or minus, a t -val, excuse me, a z value for that .005 in the upper tail.
00:29
And we have our population standard deviation divided by the square root of n.
00:34
And when we do that calculation, we find that the gas mileage we would believe is approximately 31 .1 miles per gallon to about 35 .5 miles per gallon, which this number is inside here, so they do seem to be pretty consistent at that.
00:51
But now we want to do a hypothesis test.
00:54
And you said to your four steps, and i don't know exactly what your four steps are, but let's just go through.
00:59
To first of all give our hypotheses.
01:01
We'll assume that the gas mileage is 32 miles per gallon and then you're claiming or the person is claiming that they believe it may be higher.
01:10
So they test 43 vehicles and they find that they get a gas mileage of 33 .3 on the average.
01:18
So for our distribution, our assumption is that 32 is the mileage and the standard deviation for that distribution because of the central limit theorem would be 5 .5 divided by the square root of 43.
01:36
And our 5 % is going to be all in the upper tail since we're doing a greater than test.
01:42
And that z value, because of this being population standard deviation for individuals, is given as 5 .5.
01:51
That z value is 1 .645...