Question

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

Suppose this basic test is carried out for a random sample of 75 professional golfers. Each golfer swings the four clubs and has to decide which club is heavier, and 23 out of the 75 golfers pick out the correct club as being heavier.   We want to conduct a hypothesis test where our null hypothesis is that these golfers are just guessing and the alternative hypothesis is that a greater proportion (p) of professional golfers than expected under random chance can recognize the heaviest of the four clubs. In symbols, our hypotheses would be

H_o: p = 0.25

H_a: p > 0.25

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

2. From the above information, what will the sample proportion (or p) be? Please compute this below and round to two decimal places.

3. Use the following formula to compute the test statistic.

z=p-pp(1-p)n

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

5. If our significance or alpha level is 0.05, should we consider the results of this hypothesis test to be statistically significant? Please explain why or why not.

Answer 1

given data are:-

sample size (n ) = 75

x = number of golfers who picked out the correct club as being heavier = 23

hypothesis:-

the null hypothesis is p =0.25, as the null hypothesis is that these golfers are just guessing..that is they are choosing 1 club among the 4 clubs ..just by guessing..so the probability of choosing any one club is 1/4 = 0.25.

the sample proportion is:-

the test statistic be:-

p value be:-

[ using standard normal table]

decision:-

p value = 0.1151 > 0.05 (alpha)

so, we fail to reject the null hypothesis and conclude that the results of this hypothesis test is not statistically significant.

*** if you have any doubt regarding the problem please write it in the comment box.if you are satisfied please give me a LIKE if possible...