Question

A student bought 6 bags of Fritos from different stores and vending machines, and then carefully weighed each bag. The weights (in grams) are: 35.5, 35.3, 35.1, 36.4, 35.4, 35.5

The student wishes to estimate the mean weight of a bag of Fritos.

a) Check the assumptions needed to make an inference about the mean weight.

b) Construct a 95% confidence interval for the mean weight of a bag of Fritos. Explain your work.

Answer 1

a)

• In theory, the data should be drawn from a normal distribution or it is a large sample
• The data must be reasonably random.
• The sample must be less than 10% of the population.

b)

sample mean, xbar = 35.53
sample standard deviation, s = 0.4502
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 * 0.4502/sqrt(6)
ME = 0.473

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (35.53 - 2.571 * 0.4502/sqrt(6) , 35.53 + 2.571 * 0.4502/sqrt(6))
CI = (35.06 , 36)