Question A government studied the output of farms in their c

Question: 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 and 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.

(1) Determine whether the following statements are true or false, and carefully explain your reasoning.*

a. 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.)

b. We are 95% confident that the average change in yield for these 70 farms is between -2% and 4.5%. (Be sure to include a precise description of what 95% confident means in this context.)

c. 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.)

d. 95% of the samples have a sample mean between -2% and 4.5%.

e. A 99% confidence interval would be narrower than the 95% confidence interval since we need to be more sure of our estimate.

f. 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.

(2)Compute the sample mean and margin of error.

(3)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.

(4) 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 a both 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.

Can you help me with these 4 questions? Many thanks!!! :)

Solution

b. We are 95% confident that the average change in yield for these 70 farms is between -2% and 4.5%.

TRUE.

The required CI is: (-2%,4.5%)