00:01
So for this problem, we are told that a shipping firm suspects that the mean life of a certain brand of tires, of tire used by its trucks is less than 31 ,000 miles.
00:11
So to check this claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 30 ,250 with a standard deviation of 1 ,000 miles.
00:21
At alpha equals 0 .05, we are to test the shipping firm's claim, where for part one, we're asked to state to the null hypothesis and the alternative hypothesis.
00:30
So in this case, the null hypothesis is that the mean lifetime is greater than or equal to 31 ,000 miles.
00:40
And the alternate hypothesis is that the mean lifetime is strictly less than 31 ,000 miles.
00:48
For part two, we're asked to identify the significance level.
00:51
That is alpha equals 0 .05.
00:54
Part three we're asked to calculate the test statistic in this case we have that since it's a small sample and we don't know the population standard deviation this would be the t score which is going to be given by the sample mean x bar minus the null hypothesized mean mu not over the sample standard deviation divided by the square root of the sample size so x bar was 30 ,000 or that was 32 50 or 30 ,250, and we subtract off 31 ,000.
01:28
We divide that by, now our sample standard deviation was 1 ,000.
01:33
We divide 1 ,000 by the square root of the sample size, 18, which here.
01:40
We get a t score of negative 3 .18.
01:45
Then, for part 4, we're asked to sketch a graph and label completely the test statistically p -value, etc.
01:54
So, what i'll do here is, let's see.
02:03
So i'll plot this out explicitly...