A journalist once wrote aboutTiger Woods’ ability to detect subtle differences in golfequipment. Tiger Woods was sent four golf clubs to test. The fourclubs looked identical, but one was heavier than the rest by justtwo grams (about the weight of a dollar bill). Tiger Woods swungeach of the four clubs and quickly declared, “This one’s heavier.”He was right.

Suppose this basic test is carriedout for a random sample of 75 professional golfers. Each golferswings the four clubs and has to decide which club is heavier, and23 out of the 75 golfers pick out the correct club as beingheavier.   We want to conduct a hypothesis test where ournull hypothesis is that these golfers are just guessing and thealternative hypothesis is that a greater proportion(p) of professional golfers than expected underrandom chance can recognize the heaviest of the four clubs. Insymbols, our hypotheses would be

H_o: p = 0.25

H_a: p >0.25

1. Why is the null hypothesis that p = 0.25?

1. From the above information, what will the sample proportion (orp) be? Please compute this below and round to two decimalplaces.

1. Use the following formula to compute the teststatistic.

z=p-pp(1-p)n

1. Based on what you see upon looking up the test statistic inTable B, what should the p-value be?

1. If our significance or alpha level is 0.05, should we considerthe results of this hypothesis test to be statisticallysignificant? Please explain why or why not.