Question

The United States Golf Association test golf balls to ensure that they conform to the rules of golf (they do not go too far). Balls are tested for weight, diameter, roundness and overall distance. The overall distance test is conducted by hitting balls with a driver swung by a mechanical device known as “Iron Byron” after the legendary great Byron Nelson, whose swing the machine is said to emulate. A total of 100 distances were collected and are available in the Excel file provided with this homework.

a. Using α = 0.05, test the hypothesis H0 : µ ≤ 260 H1 : µ > 260 and provide your conclusion.

b. Calculate and report the p-value for this test. c. Compute the power of the test if the true mean distance is 270 yards.

261.3	258.1	254.2	257.7	237.9	255.8	241.4	244.3	241.2	254.4	273.0	250.2	276.1
259.4	270.5	270.7	272.6	274.0	260.7	260.6	272.2	251.1	232.1	240.8	255.8	277.8
265.7	255.1	233.7	253.7	264.5	245.5	280.3	248.6	267.0	271.5	276.6	285.3	266.8
270.6	268.9	263.5	262.2	255.8	279.6	272.7	278.7	273.4	242.9	264.5	255.4	268.5
274.2	267.4	244.5	252.0	264.0	237.8	261.0	236.0	247.7	273.6	264.5	240.5
261.4	253.6	251.8	280.3	268.3	278.5	260.0	271.2	254.8	256.1	226.8	255.0
254.5	234.6	259.5	274.9	272.1	273.3	279.3	279.8	272.8	251.6	255.3	273.2
283.7	263.2	257.5	233.7	260.2	263.7	252.1	245.6	270.5	256.8	266.6	251.4

Answer 1