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

ID: 3204704 • Letter: Q

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.

Part C: Suppose a more comprehensive study shows the average yield for all farms in the country during 2015 turns out to be -4% with a standard deviation of 2.5%, and the data look nearly normal. Give both a qualitative and quantitative argument about what is likely to happen to the yield on the 70 farms from the first study during 2016. Be sure to discuss the merits of any assumptions you make.

Explanation / Answer

1. Here LCL=-2=xbar-E and UCL=4.5=xbar+E

Now it is given that z=1.96 as 95% CI and

Solving UCL and LCL we get -2+4.5=2xbar

So xbar=1.25

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