Problem 4 In lecture 5 we showed that is a confidence interval for Bk with cover

Question

Problem 4 In lecture 5 we showed that is a confidence interval for Bk with coverage probability a or confidenoe (same thing). We also showed that a test of H0 : .-Buo with significance level (type 1 error probability) rejects Ho if > ta with with coverage probability or confidence coefficient 10 kPko a. Show that we do not reject Ho 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 , as given), then we oltain the confidence interval above. If the tst is at a 5% significance level, what is the coverage probability of the confidence interval?

Explanation / Answer

(a) In question, we have confidence interval of beta k with coverage probability and confidence coeffiecnt 10alpha%. When confidence interval is 95%, this indicate that out of 100 there are 95 chances to true value of beta k include in study 95% confidence interval means .95=1-alpha

probability of confidence interval=1-alpha

where 95% convert into simple number is .95.

.95=1-alpha,    alpha=.05

(b) as we discussed earlier, formula is-

probability of confidence interval=1-alpha

confidence interval=1-.05

confidence interval=.95= 95%

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