Question

Trade​ associations, such as a dairy​ association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per capita consumption of milk and wanted to be 95​% confident that the estimate was no more than 0.57 gallon away from the actual​ average, what sample size is​ needed? Past data have indicated that the standard deviation of consumption is approximately 2 gallons.

Answer 1

Answer:  48

Step-by-step explanation:

As per given , we have

Confidence level : $1-\alpha=0.95$

Significance level : $\alpha=0.05$

Using z-value table , the critical z-value =$z_{\alpha/2}=z_{0.025}=1.96$

Margin of error : E =0.57 gallon

Prior standard deviation : $\sigma=2\text{ gallons}$

Required minimum sample would be :

$n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2\\\\ =(\dfrac{1.96\times2}{0.57})^2\\\\=47.2957833179\approx48$

Hence, the required minimum sample size = 48