STA 6166 Homework Assn #4 Spring 2005 1. High performance automobile engines are advertised to have 235 horsepower. A purchaser of the engines obtained actual horse power readings on 15 engines from a large shipment of engines, yielding the data: HP 230 236 240 230 235 230 237 240 233 236 229 230 234 237 233 Perform a statistical test of the null hypothesis H0:µ=235 versus the alternative hypothesis Ha:µ<235 to check whether the mean horsepower of this shipment of engines is the advertised 235, or less than the advertised horsepower. From previous records, it is known that σ = 4. Use a type 1 error of α=0.05. 2. Compute the power of your test in problem 1 for values of true horsepower equal to 230, 231, 232, 233, and 234. Plot the power curve in a graph. Assume σ = 4. Do you believe the purchaser has a good chance of detecting an inferior shipment of engines if the mean horsepower for the shipment is really 232 instead of the advertised 235?3. Suppose you purchased one engine from the shipment. What is the probability that the horsepower of your engine will be less that 230, assuming the true mean for the shipment is 235? 232? 230? Assume the horsepower values are approximately normally distributed. 4. A new shipment of engines has arrived. How many engines must be tested in order to detect a difference of five horsepower from the advertised 235 with statistical power of .80 using α = .05? Assume σ = 4. 5. Compute the p-value of the test in problem 1, and interpret the
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