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

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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.

Describe some scenarios in which it might only be possible to gather data from 70 farms, rather than every farm, such that we need to use statistical inference.

Explanation / Answer

Question1:

Mean is around 1.25%

we can also find out the standard deviation from the given 95% confidence interval

Possible reasons that data from every farm cannot be gathered:

1) Cost incurred from collecting the data from all the farms is more

2) Since the farms from a particaular region can bias the whole population, it is good that we take a random sample where the weight to biased sample can be reduced.

3) The results form Statistical inference for a sample will be more or less equal to that of population

There are methods in Statistical inference where we can test how different is sample from the population, tests like student t test can be used

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