A statistics instructor randomly selected four bags of oranges; each bag labeled 10 pounds, and weighed the bags. They weighed 10.2, 10.5, 10.3, and 10.3 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. 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. I am 95% confident that the population mean is between ____ and ____.
ii. There is a 95% chance that all intervals will be between ___ and ___.
iii. I am 95% confident that the sample mean is between ___ and ___.
b. Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer.