Question

A company tested 11 random brands of vanilla yogurt and found the number of calories per serving given below.​ (Note that more than 110 different brands of vanilla yogurt​ exist.)

140   150    160    130    110    100    160    150    110    130    100    

1) Find a​ 95% confidence interval for the average calorie content of vanilla yogurt per serving.

2) Interpret this interval for someone looking to buy yogurt

A. A randomly selected serving of yogurt has a​ 90% chance of having a calorie count within the interval.

B. There is a​ 90% chance that the true mean number of calories per serving of yogurt is within the interval.

C. We can be​ 90% confident that the interval contains the true mean number of calories per serving of yogurt

D.​ 90% of yogurts have a calorie content per serving that is within the interval.

  

Answer 1

a)

sample mean, xbar = 130.91
sample standard deviation, s = 23.001
sample size, n = 11
degrees of freedom, df = n - 1 = 10

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.228

ME = tc * s/sqrt(n)
ME = 2.228 * 23.001/sqrt(11)
ME = 15.451

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (130.91 - 2.228 * 23.001/sqrt(11) , 130.91 + 2.228 * 23.001/sqrt(11))
CI = (115.5 , 146.4)

b)

C. We can be​ 90% confident that the interval contains the true mean number of calories per serving of yogurt is between 115.5 and 146.4