Question

The company Merque is planning on launching a new sugar substitute, the YXL10. The company wants to estimate the proportion p of customers that would be allergic to the YXL10. Though encouraging experiments on rats seem to advocate this proportion does not exceed 40%, nothing is yet known regarding humans. Merque wants to test the YXL10 on a random sample of adults in order to estimate the proportion p with a margin of error, which 98 times out 100 does not exceed 0.005. What is the required sample size to guarantee the desired precision? (Hint: since no estimation is available for p, use the conservative value p=0.5.)

Answer 1

p = q = 0.5

For 98% confidence, z = 2.33

E = 0.005

Hence,

Sample size required

n- (0.5) (0.5)(2.332 0,005

n = 54289