Question

A statistics instructor randomly selected four bags of​ oranges, each bag labeled 10​ pounds, and weighed the bags. They weighed 10.4, 10.7, 10.3​, and 10.8 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.

What are the lower and upper bounds of this confidence interval?

Answer 1

The CI is calculated using the formula x-bar +/- t-alpha/2 * sigma / sqrt(n)

x-bar is the average of the numbers = 9.525
sigma is the standard deviation of the numbers = 0.15
Since there are a small number of samples you have to use the student t distribution to calculate t-alpha /2. The number of samples is 4, so the degrees of freedom is 3. You want a 95% CI. Using the table at the web site http://www.sjsu.edu/faculty/gerstman/Sta...
t-alpha/2 is 3.182

So the CI is 9.525 +/- 3.182 * 0.15 / sqrt(4) = (9.29, 9.76)

Answer 2

Hope that helps^^

Answer 3

Thank you so much!