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 $159$ golfers be chosen so that their mean driving distance is $255.9$ yards. The population standard deviation is $47.8$. Use a 5% significance level.

Calculate the followings for a hypothesis test where $H_0: \mu = 260$ and $H_1:\mu < 260$ :

(a) $\$ The test statistic is $\$
(b) $\$ The P-Value is

The final conclustion is

Your overall score for this problem is