Need Help..Business Stats...*99% Confidence tht the sample prop. has a margin of error of 0.035*?

Spalding Corp wants to est. the proportion of golfers who are left handed. How many golfers must be surveyed if we want 99% confidence that the sample prop. has a margin of error of 0.035?


A.)Assume-there is no avail. info. that could be used as an est. of the sample prop.


B.) Assume that we have an est. of the sample prop. from a prev. study that suggests 17% of golfers are lefties.


C.)Assume-instead of using randomly selected golfers, the sample data are obtained by asking tv viewers of the golf channel to call an 800 # to report whether they are left or right handed. How are the results affected?

Need Help..Business Stats...*99% Confidence tht the sample prop. has a margin of error of 0.035*?
Confidence intervals are used to find a region in which we are 100 * ( 1 - α )% confident the true value of the parameter is in the interval.





For large sample confidence intervals about the population proportion you have:





pHat ± z * sqrt(phat * (1- phat) / n)





where phat is the sample proportion


z is the zscore for having α% of the data in the tails, i.e., P( |Z| %26gt; z) = α


n is the sample size





To find the sample size needed for a confidence interval of a given size we need only to concern ourselves with the error term and the width of the interval.


We know that the interval is centered at phat so we need to find the value of n such that





z * sqrt(phat * (1-phat) / n) = width.





The z-score for a 0.99 confidence interval is the value of z such that 0.005 is in each tail of the distribution.


z= 2.575829





The equation we need to solve is: z * sqrt(phat * (1-phat) / n) = width





n = phat * (1 - phat) * (width / z) ^ -2.





If we don't know anything about phat and are still asked to find the sample size we let phat = 0.5. This maximizes the value of the error term and if n is sufficient for phat = 0.5, the n will be sufficient for all other values of phat.





n = 0.5 * ( 1 - 0.5 ) * ( 0.035 / 2.575829 ) ^ -2





n = 1354.061





n must be integer valued. Always take the ceiling of n so that the size of the interval will be correct.





n = 1355


























B)





n = 0.17 * ( 1 - 0.17 ) * ( 0.035 / 2.575829 ) ^ -2





n = 764.2318





n must be integer valued. Always take the ceiling of n so that the size of the interval will be correct.





n = 765























C)





since we are only looking at the left/right handedness of the golfer, it is likely that the phone in will not matter to much as there is likely no confounding variable between the ability to phone or the interest in phoning and handedness.