Question

A toy manufacturer wants to know how many new toys children buy each year. Assume a previous study found the standard deviation to be 1.5. She thinks the mean is 6.9 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.11 at the 80% level of confidence? Round your answer up to the next integer.

Answer 1

306

Explanation:

The sample size n in Simple Random Sampling is given by

`\bf n=(z^2s^2)/(e^2)`

where

z = 1.2816 is the critical value for a 80% confidence level (*)

s = 1.5 is the estimated population standard deviation

e = 0.11 points is the margin of error

so

`\bf n=(z^2s^2)/(e^2)=((1.2816)^2(1.5)^2)/((0.11)^2)=305.42\approx 306`

rounded up to the nearest integer.

(*)This is a point z such that the area under the Normal curve N(0,1) inside the interval [-z, z] equals 80% = 0.8

It can be obtained in Excel or OpenOffice Calc with

NORMSINV(0.9)