00:01
Hello students, we have given sample size n is equal to 40, sample mean x bar is equal to 42 .8, sample standard deviation s is equal to 2, population mean mu is equal to 42, alpha is equal to 0 .01.
00:19
Here we want to test the claim is to determine whether or not the new automobiles actually do average more than 42 miles per gallon.
00:28
The null and alternative hypothesis is h naught such that mu is equal to 42 against the alternative hypothesis h1 such that mu greater than 42.
00:45
It is a one tailed right tailed test.
00:48
The test statistic is t is equal to x bar minus mu divided by s by root n.
01:03
Now let us substitute the values into the formula of test statistic.
01:09
We will get t is equal to 42 .8 minus 42 divided by 2 by square root of 40 which is equal to 0 .8 by 0 .31622.
01:26
Therefore, the test statistic t is calculated as 2 .5298.
01:33
Now the degrees of freedom for the test is n minus 1 which is 39...