00:01
Our question says that a bearing used in automotive applications is supposed to have a nominal diameter of 3 .81 centimeter.
00:07
A random sample of 25 bearing is selected and the average inside diameter of this bearing is 3 .8037 centimeter.
00:14
So bearing diameter is known to be normally distributed with a standard deviation that equals to 0 .03 centimeter.
00:22
So at 1 % level of significance, is there evidence to support the claim that the average inside diameter differs from the nominal diameter let's go into our worksheet our population mean new we have that to be equals to 3 .81 centimeter the sample size ends across to 25 and the population mean new we have that to be cost to 3 .80 37 centimeter and the population standard division zigma is 0 .03 centimeter so let's take the null and the alternative hypothesis first that is the first thing to do so we have our h knot as mule is equal to 3 .81 and the the alternative hypothesis is that mew is not equals to 3 .81.
01:06
So it's time to get our test statistics.
01:09
Our test statistics can either be a z test or a t test.
01:14
So taking a look at our sample size, even though we have a sample size as low as 35 that is lesser than 30, we can see that we have the value of the population standard division, which simply implies that our test statistics is going to be a z test.
01:27
So we have a z to be across to x bar minus mule, divided.
01:32
By sigma divided by the square root of n x by in this case of us is a 3 .8037 minus 3 .81 divided by 0 .03 divided by the square root of 25 so 3 .8037 minus 3 .81 we have that to be equals to minus 0 .0063 divided by so 0 .03 divided by so 0 .03 divided by 0 .03 divided by divided by the square root of 25, we have that to be cost 0 .006.
02:10
So our z is actually equals to minus 0 .0063 divided by 0 .006 and that is minus 1 .05.
02:20
So our test statistics is minus 1 .05...