Question

Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:

130, 160, 150, 120, 90, 110, 170, 140, 110, 130, 90

If we want to create a 95% confidence interval for the average calorie count of vanilla yogurt:

a) what would be the upper bound of the confidence interval?

b) what would be the lower bound of the confidence interval?

c) what would be the critical value?

d) what would be the margin of error?

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 127.2727273

S = 26.49185123

n = 11

df = n – 1 = 10

Confidence level = 95%

Critical t value = 2.2281

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 127.2727273 ± 2.2281*26.49185123/sqrt(11)

Confidence interval = 127.2727273 ± 17.7975

Lower limit = 127.2727273 - 17.7975 = 109.48

Upper limit = 127.2727273 + 17.7975 = 145.07

Confidence interval = (109.48, 145.07)

Part a Answer: 145.07

Part b Answer: 109.48

Part c Answer: 2.2281

Part d Answer: 17.7975