An established market research consultancy has decided to check its own market p
ID: 3155081 • Letter: A
Question
An established market research consultancy has decided to check its own market profile. Out of a random sample of 100 local residents, they find that 42 have heard of their brand name. Based on this sample, construct a 99% confidence interval for the true proportion p of local residents who have heard this brand name. After constructing this interval, the chief consultant feels that it is too wide to be useful and would like to shorten the interval; however, she does not want to change the confidence level and decides instead to increase the sample size. Assuming the observed proportion stays the same, how large a sample is needed to ensure an interval with width of no more than 0.02?Explanation / Answer
a) The 99% c.i=Ps+-Zsqrt[Pu(1-Pu)/N], where Ps and Pu are sample and population proportion, N is sample size, Z corresponds to z score at alpha=0.01.
=42/100+-2.58sqrt[0.5(1-0.5)/100]
=0.291 to 0.549