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.

6. In order to decrease the margin of error of a 95% confidence interval to half of what it is now we would need to double the sample size.

Explanation / Answer

6. In order to decrease the margin of error of a 95% confidence interval to half of what it is now we would need to double the sample size.

It is false, although increasing the sample size decrease the amount of margin of error but n't that double the size is exaclt half the margin of error

Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value

Here sample size in inversely proportional to the value of margin of error, it explains increasing the size increases the margin of error and the vice versa

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