Question

Students investigating the packaging of potato chips purchased 6 bags of chips marked with a net weight of 28.5 grams. They carefully weighed the contents of each​ bag, recording the following weights​ (in grams): 29.4​, 28.3​, 29.4​, 28.8​, 28.9​, 28.5.

A) Create a 95% confidence interval for the mean weight of such bags of chips:

( __ , __ ) grams -- Round to one decimal as needed.

B) Explain in context what your interval means:

- We are 95% confident that the interval contains the true mean weight of the contents of a bag of chips

- 95% of all bags of chips will have a mean weight that falls within the interval

- The interval contains the true mean weight of the contents of a bag of chips 95% of the time.

- 95% of all the chips will be contained in the interval.

C) Comment on the company's stated net weight of 28.5 grams

- Since the interval contains the stated weight of 28.5 grams, there is not sufficient evidence that the company is failing to fill the bags to the stated weight, on average.

- Since the interval is below the stated weight of 28.5 grams, there is sufficient evidence that the company is filling the bags to less than the stated weight, on average.

- Since the interval is above the stated weight of 28.5 grams, there is sufficient evidence that the company is filling the bags to more than the stated weight, on average.

Answer 1

a)

sample mean, xbar = 28.883
sample standard deviation, s = 0.4535
sample size, n = 6
degrees of freedom, df = n - 1 = 5

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.571

ME = tc * s/sqrt(n)
ME = 2.571 * 0.4535/sqrt(6)
ME = 0.476

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (28.883 - 2.571 * 0.4535/sqrt(6) , 28.883 + 2.571 * 0.4535/sqrt(6))
CI = (28.4 , 29.4)

b)
We are 95% confident that the interval contains the true mean weight of the contents of a bag of chips

c)

Since the interval contains the stated weight of 28.5 grams, there is not sufficient evidence that the company is failing to fill the bags to the stated weight, on average.