Question

# A toy manufacturer wants to know how many new toys children buy each year. Assume a...

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 7.2 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.1 at the 98% level of confidence?

Given that the standard deviation , =1.5 and margin of error, E=01 , hence by Z table given below Z score at 98 % confidence level is 2.33 Now by Minimum sample formula

$N=Z_{c}^2*\frac{\sigma^2}{E^2}=2.33^2*\frac{1.5^2}{0.1^2}=1221.5025\approx 1222$

Hence minimum sample required is 1222

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N Z2 E2 2.332 1.52 0.12 48.8601 49

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