Math 112-Worksheet #9-1 1. Graph the critical region area...

Math 112-Worksheet #9-1 1. Graph the critical region area and find the critical value(s) for each by using the table G. a) $\alpha$ = 0.01, $n$ = 17, right-tailed b) $\alpha$ = 0.025, $n$ = 20, left- tailed c) $\alpha$ = 0.01, $n$ = 13, two-tailed d) $\alpha$ = 0.05, $n$ = 27, right-tailed

Transcript

00:03 The null hypothesis for this problem will be h0, sigma square equal to 225.

00:26 And since it is given that it is two -tailed test, the alternative hypothesis h1 will be sigma square not equal to 225.

00:46 So these are our null hypothesis and alternative hypothesis.

00:58 Now we have to find the critical values.

01:04 First we will find the degrees of freedom.

01:07 Degrees of freedom equal to n minus 1.

01:11 N is given to be 14.

01:13 So degrees of freedom equal to 14 minus 1 which is equal to 13.

01:19 Since the test is 2 tailed, the area must be splited.

01:26 Alpha equal to 0 .10.

01:29 So alpha divided by 2 equal to 0 .10 divided by 2 which is equal to 0 .05.

01:46 So 0 .05 will be the right side's shaded area and 0 .05 will be the left side shaded area.

02:05 For right side critical value, we will see in the table for kayskar distribution under degrees of freedom 13 and alpha equal to 0 .05.

02:16 So the right side's critical value is 22 .362 as seen in the table for kai square distribution.

02:38 For left side's critical value, see the value under alpha equal to 1 minus this 0 .05.

02:46 So 1 minus 0 .05 is equal to 0 .95.

02:51 So see under 0 .95 for degrees of freedom 13.

02:56 The value is 5 .892 as seen in the table for the kai square distribution.

03:09 These are the required critical values, 5 .892 and 22 .362.

03:20 The region right side to the right side's critical value, that is this shaded region, is our critical region.

03:28 Also, the region to the left of the left side's critical value is our critical region.

03:34 That is these two shaded regions are our critical regions so the unshaded region is our non -critical region now for this our null hypothesis will be same that is null hypothesis is h0 sigma square equal to 225 the alternative hypothesis h1 will be as it is right -tailed test h1 will be sigma square greater than 225.

04:45 So these are our null hypothesis and alternative hypothesis.

04:50 Now degrees of freedom equal to n minus 1.

04:54 So degrees of freedom equal to 27 minus 1, that is 26.

05:03 For critical value, since it is right till it test, see the value under alpha equal to 0 .05, which is the given value of alpha and degrees of freedom.

05:19 Equal to 26.

05:21 The critical value is 38 .85 as seen in the table for the kai square distribution.

05:38 The region to the right side of the right side critical value, that is this shaded region is our critical region...

Question

Math 112-Worksheet #9-1 1. Graph the critical region area and find the critical value(s) for each by using the table G. a) $\alpha$ = 0.01, $n$ = 17, right-tailed b) $\alpha$ = 0.025, $n$ = 20, left- tailed c) $\alpha$ = 0.01, $n$ = 13, two-tailed d) $\alpha$ = 0.05, $n$ = 27, right-tailed

Please give Ace some feedback