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%% Compute Power and Sample Size for One-Sided Test % Copyright 2015 The MathWorks, Inc. %% % An employee wants to buy a house near her office. She decides to % eliminate from consideration any house that has a mean morning commute % time greater than 20 minutes. The null hypothesis for this right-sided % test is H0: $\mu$ = 20, and the alternative hypothesis is HA: $\mu$ > 20. % The selected significance level is 0.05. %% % To determine the mean commute time, the employee takes a test drive from % the house to her office during rush hour every morning for one week, so % her total sample size is 5. She assumes that the standard deviation, % $\sigma$, is equal to 5. %% % The employee decides that a true mean commute time of 25 minutes is too % different from her targeted 20-minute limit, so she wants % to detect a significant departure if the true mean is 25 minutes. % Find the probability of incorrectly concluding that the mean commute time % is no greater than 20 minutes. %% % Compute the power of the test, and then subtract the power from 1 to % obtain $\beta$. power = sampsizepwr('t',[20 5],25,[],5,'Tail','right'); beta = 1 - power %% % The $\beta$ value indicates a probability of 0.4203 that the % employee concludes incorrectly that the morning commute is not % greater than 20 minutes. %% % The employee decides tha this risk is too high, and she wants % no more than a 0.01 probability of reaching an incorrect conclusion. % Calculate the number of test drives the employee must take to obtain % a power of 0.99. nout = sampsizepwr('t',[20 5],25,0.99,[],'Tail','right') %% % The results indicate that she must take 18 test drives from a % candidate house to achieve this power level. %% % The employee decides that she only has time to take 10 test drives. % She also accepts a 0.05 probability of making an incorrect conclusion. % Calculate the smallest true parameter value that produces a detectable % difference in mean commute time. p1out = sampsizepwr('t',[20 5],[],0.95,10,'Tail','right') %% % Given the employee's target power level and sample size, her test % detects a significant difference from a mean commute time of at least % 25.6532 minutes.