Question

Suppose the heights of seasonal pine saplings are normally distributed. If the population standard deviation is 14 millimeters, what minimum sample size is needed to be 95% confidence that the sample mean is within 4 millimeters of the true population mean?​

Answer 1

Answer: 48

Explanation:

As per given , we have

Population standard deviation :
`\sigma=14\text{ millimeters}`

Significance level :
`\alpha=1-0.95=0.05`

Critical value for 95% confidence interval (refer to z-value table) =
`z_(\alpha/2)=1.96`

Margin of error :
`E=4\text{ millimeters}`

Formula , we use to find the sample size :

`n=((z_(\alpha/2)\cdot\sigma)/(E))^2\\\\ n=((1.96\cdot 14)/(4))^2\\\\ n=(6.86)^2=47.0596\approx48`

Hence, the required sample size = 48