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 235 yards on average. Suppose a random sample of 193 golfers be chosen so that their mean driving distance is 240.6 yards, with a standard deviation of 47.3. Conduct a hypothesis test where H_0 : mu = 235 and H_1 : mu > 235 by computing the following: (a) test statistic (b) p-value p = (c) If this was a two-tailed test, then the p-value is

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   235  
Ha:    u   >   235  
              
As we can see, this is a    right   tailed test.      
a)

              
Getting the test statistic, as              
              
X = sample mean =    240.6          
uo = hypothesized mean =    235          
n = sample size =    193          
s = standard deviation =    47.3          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.644771381 [ANSWER]

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b)          
              
Also, the p value is, as this is right tailed,              
              
p =    0.050008483   [ANSWER]      

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c)

If this is two tailed, the P value will double,

P = 2*0.050008483 = 0.100016966 [ANSWER]

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