Golf-course designers have become concerned that old courses are becoming obsole

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 250 yards on average. Suppose a random sample of 156 golfers be chosen so that their mean driving distance is 247.9 yards. The population standard deviation is 45.4. Use a 5% significance level. Calculate the followings for a hypothesis test where H0:=250 and H1:<250 :

(a) The test statistic is

(b) The P-Value is

The final conclustion is

A. There is sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 250

B. There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 250

Explanation / Answer

a)

test static = x -mean/std/sqrt(n)

= 247.9 - 250/45.4/sqrt(156)

= -0.5777

b)

P-value = P(Z < -0.5777 ) = 0.2817

hence there is not sufficient evidence to rejection of claim

hence choose A)

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