Question

You are constructing a marketing research study to determine what proportion of consumers between the ages of 18 and 35 own DVD players. You have randomly sample 60 individuals in that age range, and you have determined that 11 of them own DVD players.

a.Find the 90% confidence interval for the proportion.

b. Suppose that your contract for the study requires that you estimate the proportion within plus or minus 0.05 with 90% confidence. How many additional subjects would you need to sample to obtain that level of precision?

Answer 1

a)

Sample proportion = 11 / 60 = 0.183

Margin of error at 90% confidence = Z/2 * sqrt [ p (1 - p) / n]

= 1.645 * sqrt [ 0.183 ( 1 - 0.183 ) / 60 ]

= 0.082

90% confidence interval is

- E < p < + E

0.183 - 0.082 < p < 0.183 + 0.082

0.101 < p < 0.265

90% CI is ( 0.101 , 0.265 )

b)

Sample szie = Z2/2 * p ( 1 - p) / E2

= 1.64492 * 0.183 ( 1 - 0.183) / 0.052

= 162.01

sample size = 163 (Rounded up to nearest integer)

Additional sample required = 163 - 60 = 103