00:01
Okay, so here in part a, we're given the sample n is 36.
00:04
So the degrees of freedom is 36 minus 1, which is 35.
00:08
The sample mean x bar is 44, and the sample standard deviation is 5 .2.
00:14
The hypotheses to be tested are h -0, which is mu greater than or equal to 45.
00:20
And then the alternative hypothesis would be mu is less than 45.
00:24
So here the test statistic is given by t is equal to x bar.
00:30
Minus mu not, that's going to be 44 minus 45, and then divided by s minus the square root of n, which is going to be 5 .2 divided by the square root of 36 or 6, which is going to be equal to negative 1 .15.
00:48
So then we get the area under the t distribution curve to the left of negative 1 .15 is the same as the area under the curve to the right of t equals 1 .15, which we get from the t table, and our degrees of freedom, which we then get that t is going to be equal 1 .15, is between 0 .852 and 1 .306.
01:11
So then the area in the upper tail roll, we see the area to the tail of the right of t equals 1 .15 is between 0 .2 and 0 .1, which we then get the p value must be between 0 .20 and 0 .10.
01:30
So given that alpha is 0 .05, we have that our p value is going to be greater than alpha.
01:39
So therefore, we then fail to reject the null hypothesis at a 1 % level of significance.
01:50
Then for part b, we're given the size of the sample n is 36.
01:56
We get our degrees of freedom then as 36 minus 1.
02:00
So that's 35.
02:02
And then our sample mean x bar is 43.
02:06
And our sample standard deviation is 4 .6.
02:12
So then the hypothesis to be tested again, h0, mu grade, then equal to 45, and the alternative, which be mu less than 45...