Question

Ha:μ<85 A sample of 140 is used and the population standard deviation is 10, Compute the p-value and state your conclusion for each of the following sample results. Use a-0.01 Round z value to two decimal places and p-value to four decimal places. If your answer is zero, enter "O". Enter negative value as negative number a. 82.5 z value p-value conclusion reject b.82 Ho z value p-value conclusion reject Ho C.80 z value p-value conclusion reject d. 86.5 Ho z-value p-value conclusion do not reject

Answer 1

Given a sample size (n) = 140 population standard deviation (sigma) = 10 population mean (mu) = 85 alpha = 0.01 Null Hypothesis H_0: mu greaterthanorequalto 85 Alternative Hypothesis H_a: mu < 85 Level of significance alpha = 0.01 x = 82.5 z test = x - mu/(sigma/squareroot n) implies 82.5 - 85/(10/squareroot 140 implies - 2.5 0.845 implies - 2.959 p (z < - 2.959) = 0.001543 therefore p value = 0.001543 < 0.01 therefore reject H_0 x = 82 z_value x - mu/sigma/v mu implies 82 - 85/10/squareroot 140 implies - 3.000.0.845 implies - 3.355 therefore p(z < - 3.355) = 0.000397 therefore p value < 0.01 therefore reject H_0 \r\n x = 80 z_value = x - mu/(sigma/squareroot n) implies 80 - 875/(10/v 140) implies - 5/0.845 z_value = -5.917 p(z < - 5.917) = 0.00001 p_value = 0.00001 < 0.01 therefore reject H_0 x = 86.5 z_value = x - mu/(sigma/squareroot n) implies (86.5 - 85)/(10/squareroot 140 implies 1.5/0.845 = 1.775 z_value = 1.775 p(z > 1.775) = 0.037949 > 0.01 therefore