A manager at a local fast food restaurant is concerned about customers who ask f

Question

A manager at a local fast food restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a soft drink instead of filling the cup with water. The manager selected a random sample of customers who asked for a water cup and found a 95% confidence interval of (.20, .40) for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. Find the observed sample proportion, the margin of error of the confidence interval, the standard error of , and the number of customers that were sampled. Clearly show your work and label each value.

Explanation / Answer

sample proportion p is given as (0.2+0.4)/2=0.3 (it falls in the average of the upper and lower bound)

for 95% confidence, the z value is 1.96

thus margin of error (ME) is upper limit - p= 0.4-0.3=0.1

standard error SE is given as ME=z*SE

0.1=1.96*SE

thus SE is 0.05102

SE=sqrt(p*(1-p)/N)

0.05102=sqrt(0.3*(1-0.3)/N)

N is 0.3*0.7/(0.05102)^2=80.675

thus N is 81

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