Question

Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 235 yards on average. Suppose a random sample of 118 golfers be chosen so that their mean driving distance is 239.8 yards, with a standard deviation of 43.6. Conduct a hypothesis test where H0:μ=235 and H1:μ>235 by computing the following:

(a) test statistic?

(b) p-value?

(c) If this was a two-tailed test, then the p-value is?

Answer 1

a) The test statistic z = ()/(s/)

                                  = (239.8 - 235)/(43.6/)

                                  = 1.20

b) P-value = P(Z > 1.20)

                 = 1 - P(Z < 1.20)

                = 1 - 0.8849

                = 0.1151

c) P-value = 2 * P(Z > 1.20)

                 = 2 * (1 - P(Z < 1.20))

                = 2 * (1 - 0.8849)

               = 2 * 0.1151 = 0.2302