The weights of four randomly chosen bags of horse carrots, each bag labeled 20 pounds, were 20.5, 19.8, 20.8, and 20.0 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of horse carrots. Use technology for your calculations.

a. Decide whether each of the following three statements is a correctly worded interpretation of the confidence interval, and fill in the blanks for the correct option(s).

i. 95% of all sample means based on samples of the same size will be between ___ and ____.

ii. I am 95% confident that the population mean is between ____ and ____.

iii. We are 95% confident that the boundaries are ____ and ____ .

b. Can you reject a population mean of 20 pounds? Explain.