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.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-12T10:34:53+01:00

Answer: 48

Step-by-step explanation:

As per given , we have

Confidence 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 gallon

Prior 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