Oranges

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.