Grade: Quiz Chapter 12 2 points each[an incorrect conclusion is -1 point] Note:All the 's below should be ², but the software won't allow both a sub & superscript on the same character. For the following Hypothesis Tests below : (a) State the null hypothesis, if not given. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding H₀? (e) Your conclusion. 1. For purposes of the F distribution, which of these two variances should be in the numerator: 12.6 or 15.3?Why? 2.The mean quantity of milk produced by Guernsey & Holstein cows at Cold Comfort Farm is about the same, but the variation in output is quite a bit different as shown by the standard deviation of breed output from a sample of 10 Guernsey & 15 Holstein : _Guernsey = 1.8 & _Holstein = 1.2 Conduct an ANOVA F test to see if the Guernsey variation is really different from Holstein or simply due to pure chance.Use = .05. (a)Ho: (b)Reject H_o when (c)F = (d)Ho is (e) Assignment Chapter 12 Exercise 2: What is the critical F value for a sample of four observations in the numerator and seven in the denominator? Use a one-tailed test and the .01 significance level. F = Exercise 4: The following hypothesis is given. Ho:₁² = ₂² A random sample of five observations from Population 1resulted in a standard deviation of 12.A random sample of seven observations from Population 2 showed a standard deviation of 7.At the .01 significance level, is the variation really different? (a)Insert H₁: (b)Reject H_o when (c)F = (cdHo is (e) Exercise 6: A stockholder at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a standard deviation of 3.9 percent.The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent.A the .05 significance level, can we conclude that the variations are different? (a)Ho: (b)Reject H_o when (c)F = (d)Ho is (e)