Test each of the following hypotheses by using the given...

Test each of the following hypotheses by using the given information. Assume the populations are normally distributed. a. H0: σ^2 = 20 Ha: σ^2 > 20 α = .05, n = 15, s^2 = 32 b. H0: σ^2 = 8.5 Ha: σ^2 ≠ 8.5 α = .10, n = 22, s^2 = 17 c. H0: σ^2 = 45 Ha: σ^2 > 45 α = .01, n = 8, s^2 = 4.12 d. H0: σ^2 = 20 Ha: σ^2 ≠ 20 α = .05, n = 11, s^2 = 1.2

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00:01 Hi, i'm david and i'm here to have you answered the question.

00:03 Now let me pick up your question here.

00:06 In the question here we are going to discuss about the hypothesis testing and we have the four questions a, b, c, d.

00:14 So let me split the screen onto the four equal parts.

00:24 And now in the question a, b, c and the d, in the a we will have to test the known hypothesis that the c sigma square equal to the 20 versus the alternative hypothesis, then the sigma square will greater than the 20.

00:46 Notice that this is the right -tow test.

00:49 And given the information here, we will be able to find the test statistics denoted by the k square.

00:58 The formula will be the n minus 1 times the n square over the sigma square, and then we have n equal equal to the 15 minus 1 and then we will have times the n square which is equal to the 32 divided by the sigma square will be the 20 and now if we compare this one again the answer is equal to the 14 times 32 divided by 20 and equal to the 22 and equal to the 22 2 .4.

01:37 Then the next time i will compute the p value and the p value it will equal to the probability the k -square the degree -vidum equal to 8 minus 1 will equal to the 14 that will be greater than the test statistics.

01:51 And to compute this on and use the kai -square distribution with the 14 degree freedom greater than the 22 .4.

02:02 Then we get equal to the 0 .07, 08.

02:07 And we see this b value here it is greater than the m4 equal to the 0 .05 therefore we are going to fail to reject the known hypothesis and that will be the question a.

02:28 Now for the question b we have to test the known hypothesis that the sigma squared equal to a .5 versus the alternative hypothesis that the sigma square will be not equal to the 8 .5.

02:44 And notice that this is the 2tel task.

02:50 And now again we have to compute the test statistics denoted by the k square and we will have the n will equal to 22 minus 1 times of the n square will be the 17 divided by the 8 .5 and if we compute will have the 21 times 17 divided by 8 .5...

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