MATH SOLVE

2 months ago

Q:
# 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

A:

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