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?

Accepted Solution

Answer: 758 Step-by-step explanation:Given : Mean : [tex]\mu=6.9 \text{ toys per year][/tex]Standard deviation : [tex]\sigma = 1.3[/tex]Margin of error : [tex]E=0.11\text{ toys}[/tex]Significance level : [tex]\alpha=1-0.98=0.02[/tex]Critical value : [tex]z_{\alpha/2}=2.33[/tex]Formula for sample size Β :-[tex]n=(\dfrac{z_{\alpha/2}\sigma}{E})^2\\\\\Rightarrow\ n=(\dfrac{2.33\times1.3}{0.11})^2=758.251322314\approx758[/tex]Hence, the minimum required sample size = 758