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.

Accepted Solution

Answer:  48Step-by-step explanation:As per given , we haveConfidence level : [tex]1-\alpha=0.95[/tex]Significance level : [tex]\alpha=0.05[/tex]Using z-value table , the critical z-value =[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]Margin of error : E =0.57 gallonPrior standard deviation : [tex]\sigma=2\text{ gallons}[/tex]Required minimum sample would be :[tex]n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2\\\\ =(\dfrac{1.96\times2}{0.57})^2\\\\=47.2957833179\approx48[/tex] Hence, the required minimum sample size = 48