Question

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 81 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 16.4 and a standard deviation of 3.5. What is the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

< μ <

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 16.4

S = 3.5

n = 81

df = n – 1 = 80

Confidence level = 90%

Critical t value = 1.6641

(by using t-table)

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

Confidence interval = 16.4 ± 1.6641*3.5/sqrt(81)

Confidence interval = 16.4 ± 0.6472

Lower limit = 16.4 - 0.6472 = 15.7528

Upper limit = 16.4 + 0.6472 = 17.0472

Confidence interval = (15.7528, 17.0472)

15.8 < µ < 17.0