Steps for computing the power 1 Select a specific value for the alternate hypothesis 2 Compute the rejection region 3 Compute the probability that the test statistic falls within the rejection region if the alternate hypothesis is true A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles a State the null and alternate hypothesis Which is true b It is decided to reject Ho if the sample mean is less than 49 400 Find the level and power of this test c If the test is made at the 5 level what is the power A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles a State the null and alternate hypothesis Which is true H 0 50000 miles H1 50000 miles H1 A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles b It is decided to reject Ho if the sample mean is less than 49 400 Find the level and power of this test H 0 50000 miles First we need to find the level How z What is the level 50 000 49 400 1 2 500 0 1151 H1 50000 miles A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles H 0 50000 miles H1 50000 miles Level 0 1151 Now we need to find the power How What is the critical point z Power 0 42 49500 49 400 0 2 500 A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles c If the test is made at the 5 level what is the power Critical point Power z 50000 x 1 65 500 x 49 175 z 49500 49 175 0 65 500 Power 0 2578 A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles How many tests should be made so that the power is 0 8 at the 5 level 50000 x 1 65 5000 n 5000 x 50000 1 65 n z x 49 500 0 84 5000 n 5000 x 49500 0 84 n z A tire company claims that the lifetimes of its tires average 50 000 miles The standard deviation of tire lifetimes is known to be 5000 miles You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50 000 miles against the alternative that it is less Assume in fact that the true mean lifetime is 49 500 miles How many tests should be made so that the power is 0 8 at the 5 level 5000 5000 49500 0 84 n n 4200 8250 500 n n n 620 x 50000 1 65 STATIC AND DYNAMIC CHARACTERISTICS OF SIGNALS INPUT sensor transducer Signal A MEASUREMENT SYSTEM Signal B OUTPUT Signal C Signal just associated with transmission of information Important Questions What is the dynamic range of the measurement system What is the frequency response of the measurement system What are the characteristic of the signal from your sensor transducer Are you looking for a static or dynamic response