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.

Part A: Determine whether the following statements are true or false, and carefully explain your reasoning.

1. This confidence interval is not valid as we do not know the population distribution of the change in yield of all farms in the country. (If false, include any additional information that would change your answer.)

Explanation / Answer

False.

CI is valid.

Confidence interval is always based on sampling distribution only (when population is unknown). Its interpretation is if keep on sampling between range of yields -2% and 4.5%, we will get the true population yield in 95% of the cases.

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