Question

Ferric chloride is used as a flux in some types of extraction metallurgy processes. This material is shipped in containers, and the container weight varies. It is important to obtain an accurate estimate of mean container weight. Suppose that from long experience a reliable value for the standard deviation of flux container weight is determined to be 4 lb. How large a sample would be required to construct a 95% two-sided confidence interval on the mean that has a total width of 1 lb?

Answer 1

Answer: 222

Step-by-step explanation:

As considering the given description, we have

Population standard deviation: $\sigma=4$

Margin of error : E = half of width of confidece interval

=$\dfrac{1}{2}\times1=\dfrac{1}{2}=0.5$

Critical value for 95% confidence interval : $z_{\alpha/2}=1.96$

Formula to find the sample size : $n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2$

i.e. $n=(\dfrac{(1.86)\cdot (4)}{0.5})^2$

$=(14.88)^2=221.4144\approx222$

Hence, the required minimum sample size = 222