You need to take a random sample of boat owners to determine within plus or minu

Question

You need to take a random sample of boat owners to determine within plus or minus l hour how much time they spend on boat-related activities during summer months. A similar survey conducted in 1992 found an average time of 18.3 hours month with a standard deviation of 7.6 hours. That survey had a sample size of 326 boat owners. If you wanted to be 90% confident of your findings for this survey, how large a sample should you have? How large should the sample be for 96% confidence? A make of personal care products wants to know, within 2%, the percentage of women in the U.S. who have tried its new cologne, Private Passions. Trial rates for similar new products run about 10%. How large a sample would be needed to make the estimate with 90% confidence?

Explanation / Answer

1) here margin of error E=1

std deviation =7.6

for 90% CI, z=1.64485

hence sample size=(z*std deviation/E)2~157

for 96% CI, z =2.0537

hence sample size=(z*std deviation/E)2~244

2)for 90% CI, z=1.66485

margin of error E=0.02

and p=0.1

hence sample size=p(1-p)(Z/E)2 ~609

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