Question

Exercise 12-4 (L012-1) The following hypotheses are given. A random sample of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. At the 0.01 significance level, is there more variation in the first population? (Round your answer to 2 decimal places.)

Answer 1

The Null and Alternative hypothesis are as follows: 2 Null hypothesis, H.:01 So Alternative hypothesis, H,:01 > 0 Consider a random sample of 5 observations form the first population resulted in the standard deviation of 12. Consider a random sample of 7 observations from the second population resulted in the standard deviation of 7. The level of significance is, a = 0.01 Calculate test statistic. cla = 2.94 Test statistic: 94 The numerator and denominator degrees of freedom are as follows: dfv = n, -1 = 5-1 = 4 dfp = n2 - 1 = 7-1

From the standard F table values, observe that the critical value of F for the 1% level of significance and (4, 6) degrees of freedom is 9.15 Compare the calculated value with the critical value. Here, the calculated value is less than the critical value so fails to reject the Null hypothesis. Decision: fail to reject or cannot reject H Note: Options are not given, so I given the two options in the answer choice as best of my knowledge.