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 260 yards on average. Suppose a random sample of 181 golfers be chosen so that their mean driving distance is 258.2 yards. The population standard deviation is 46.5.

Use a 5% significance level. Calculate the followings for a hypothesis test where H0:=260 and H1:<260 :

(a) The test statistic is

(b) The P-Value is

The final conclustion is (A) There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260 OR (B). There is sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260

Explanation / Answer

here null hypothesis:H0:=260

alternate hypothesis:H1:<260

a) std error of mean =std deviation/(n)1/2 =46.5/(181)1/2 =3.4563

therefore test statistic =(X-mean)/std error =(258.2-260)/3.4563=-0.5208

b) for above test statistics ; p value =0.3013

as p value is greater then 0.05 level; we can not reject null hypothesis.

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

please revert for any clarificaiton required .

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