SOLUTION: A producer of materials that are used in Laboratories has a sampling problem. One important category of his products is of two types; alpha and beta. Beta type is relatively new an

Question 74947: A producer of materials that are used in Laboratories has a sampling problem. One important category of his products is of two types; alpha and beta. Beta type is relatively new and is both costly and perishable, so it�s important to produce it in small it in qualities closely in line with market demand. Laboratory technology and preferences seem to have been changing rapidly in favour of beta type, so past sales records offer very little basis for forecasting. The manufacture�s current guess is that 60 % of the combines sales of the two products next year maybe of beta type but is going to confirm his hypothesis by having sales representative call on a sample of buyers to learn how much alpha and beta they intend to buy.
How large a sample size would they call if he the manager decided that tolerable error in estimating error in estimating the population proportion is not to be greater than 2 % at confidence level of 99 % .

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The manufacture�s current guess is that 60 % of the combines sales of the two products next year maybe of beta type but is going to confirm his hypothesis by having sales representative call on a sample of buyers to learn how much alpha and beta they intend to buy.
How large a sample size would they call if he the manager decided that tolerable error in estimating error in estimating the population proportion is not to be greater than 2 % at confidence level of 99 % .
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E = z*sqrt(pq/n)
Interchange E and sqrt(n) to get:
sqrt(n) = (z*sqrt(pq))/E
Let P=0.6, based on the guess.
sqrt(n) = (2.326sqrt(0.6*0.4))/0.02
sqrt(n) = 5.698365...
n=32 when rounded to a whole number
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Cheers,
Stan H>
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