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.

3. We are 95% confident that the average change in yield for all farms in the country is between -2% and 4.5%. (Be sure to include a precise description of what 95% confident means in this context.)

Explanation / Answer

TRUE

Because 95% of the time, when we calculate a confidence interval in this way, the true mean will be between the two values. 5% of the time, it will not. Because the true mean (population mean) is an unknown value, we don’t know if we are in the 5% or the 95%. BUT 95% is pretty good so we say something like

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