Question 1: A government studied the output of farms in their country over the c

Question

Question 1: A government studied the output of farms in their country over the course of a year in an attempt to understand the impact of new policies. They want to estimate the average change in yield from Jan. 1, 2015 to Dec. 31, 2015. A simple random sample of 70 farms (out of more than 700 total) was taken, and the percent change in total yield was measured over that period. A 95% confidence interval based on this sample is (-2%, 4.5%), which is based on the normal model for the mean.

Compute the sample mean and margin of error.

Explanation / Answer

Sample mean = xm

Margin of error = ME

For a 95% confidence interval, the range for the mean is -2% to 4.5 %

This means that xm - ME = -2% = -.02 Equation 1

and xm + ME = 4.5% = .045   Equation 2.

Adding equation 1 and 2, we get

(xm - ME) + (xm + ME) = -.02 + .045

2xm = .025, xm = 0.0125 or 1.25 %

Applying this to Equation 1

xm - ME = -.02   

0.0125 - ME = -.02

ME = 0.0125 + .02 = .0325 or 3.25%

Therefore, the sample mean is 1.25% and the margin of error is 3.25%

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