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 260 yards on average. Suppose a random sample of 184 golfers be chosen so that their mean driving distance is 257.3 yards. The population standard deviation is 44. Use a 5% significance level. Calculate the followings for a hypothesis test where H0:μ=260 and H1:μ<260 :

(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 260

B. There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
μ : Mean of population
H₀ : μ = 260
H_A : μ < 260
Standard deviation = 44

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
μ	184	257.3	3.243723	-0.83237686	0.2026

Hence,

a) Test statistic = -0.8324

b) P - value = 0.2026

Final conclusion: There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260. Option B is correct.