A production supervisor for Spalding Corporation claims that

A production supervisor for Spalding Corporation claims that the percentage of lefthanded golfers is greater than the 10% rate of people from the general population. Is the supervisors\' claim valid if in a simple random sample of 250 golfers, 38 are left-handed? Use a 0.05 Significance level to test the claim.

b) construct a 95% confidence interval estimate of the percentage of left-handed golfers. Express your answer symbolically and verbally.

c) does your confidence interval agree with your conclusion on part a)? Provide support for your answer.

Solution

(b) Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

p=38/250 = 0.152

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.152 -1.96*sqrt(0.152*(1-0.152)/250) =0.1074953

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.152 +1.96*sqrt(0.152*(1-0.152)/250) =0.1965047

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(c) Since the inerval do not include 0.1, we reject the null hypothesis.

SO your confidence interval agree with your conclusion on part (a)