Finding Critical Values Table A-7 lists critical values for limited choices of ?a. Use Table A-l to add a new column in Table A-7 (from n ? ? = 1 t? =? 8) that represents a significance level of 0.03 in one tail or 0.06 in two tails. For any particular ?n,? use ?p =? 0.5, because the sign test requires the assumption that P?(positive sign) = ?P?(negative sign) = 0.5. The probability of x or fewer like signs is the sum of the probabilities for values up to and including x ? .

Solution 22BB Step 1 By using Table A-1 we need to add new column in Table A-7 (from n = 1 to n = 8) that represents a 0.03 level of significance in one tail or 0.06 in two tails. Given, for any particular n, we have p = 0.5 because the sign test requires the assumption that P(positive sign) = P(negative sign) = 0.5. Let us denote ‘c’ as the critical value. X ~ B(n, p) For n = 1, p = 0.5 X ~ B(1, 0.5). Now, P(X c) 0.03 Therefore, at n = 1 there is no critical value. Step 2 Let us denote ‘c’ as the critical value. X ~ B(n, p) For n = 2, p = 0.5 X ~ B(2, 0.5). Now, P(X c) 0.03 Therefore, at n = 2 there is no critical value. Step 3 Let us denote ‘c’ as the critical value. X ~ B(n, p) For n = 3, p = 0.5 X ~ B(1, 0.5). Now, P(X c) 0.03 Therefore, at n = 3 there is no critical value. Step 4 Let us denote ‘c’ as the critical value. X ~ B(n, p) For n = 4, p = 0.5 X ~ B(4, 0.5). Now, P(X c) 0.03 Therefore, at n = 4 there is no critical value.