Problem 4 In lecture 5 we showed that is a confidence interval for k with covera

Question

Problem 4 In lecture 5 we showed that is a confidence interval for k with coverage probability or confidence coefficient 10cY (same thing). We also showed that a test of HO : Ao with significance level (type l error probability) a rejects Ho if >a with a. Show that we do not rejct if Bko is included in the confidence interval. What is the significance level of the test if we have a 95% confidence interval? b. Show that if we consider the values of Bko that are not rejected by the t-statistic (treat A, as given), then we obtain the confidence interval above. If the test is at a 5% significance level, what is the coverage probability of the confidence interval?

Explanation / Answer

a) The significance level (alpha) = 5%

Explanation: Here the confidence intervalis 95%. Therefore the level of significance is 5%

b) The coverage probability of the confidence interval = 95%

Explanation: Here the test was conducted at 5% level of significance

The confidence coefficient = 1 - alpha = 1-0.05 = 0.95 = 95%

Therefore the coverage probability of the confidence interval = 95%

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