Question

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 45 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 16.3 and a standard deviation of 1.3.

a) What is the 95% confidence interval for the number of chocolate chips per cookie for Big Chip cookies?
Enter your answers accurate to one decimal place. < μ <

answer ____ < μμ < ____ answer

b) Fill in the answer boxes to complete the interpretation of the confidence interval. Karen can advertise, with confident that, on average, there are between answer ___ and answer ___ chocolate chips in a Big Chip cookie at her bakery.

Answer 1

Solution :

Given that,

a) Point estimate = sample mean = = 16.3

sample standard deviation = s = 1.3

sample size = n = 45

Degrees of freedom = df = n - 1 = 45 - 1 = 44

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,44 = 2.015

Margin of error = E = t_/2,df * (s /n)

= 2.015 * ( 1.3/ 45)

Margin of error = E = 0.4

The 95% confidence interval estimate of the population mean is,  

- E < < + E

16.3 - 0.4 < < 16.3 + 0.4

15.9 < < 16.7

b)  with 95% confident that, on average, there are between 15.9 and 16.7 chocolate chips in a Big Chip cookie at her bakery.