Question

A toy manufacturer wants to know how many new toys children can buy each year. He thinks the mean is 6.9 toys per year. Assume a previous study found the standard deviation to be 1.3. How large a sample would be required in order to estimate the mean number of toys bought per child at the 98% confidence level with an error at most 0.11 toys?

Answer 1

Answer: 758

Explanation:

Given : Mean :

Standard deviation :
`\sigma = 1.3`

Margin of error :
`E=0.11\text{ toys}`

Significance level :
`\alpha=1-0.98=0.02`

Critical value :
`z_(\alpha/2)=2.33`

Formula for sample size :-

`n=((z_(\alpha/2)\sigma)/(E))^2\\\\\Rightarrow\ n=((2.33*1.3)/(0.11))^2=758.251322314\approx758`

Hence, the minimum required sample size = 758