Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 36.9 . You would like to be 99% confident that your esimate is within 4 of the true population mean. How large of a sample size is required?

Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 51 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 16.6 and a standard deviation of 3.4. What is the 98% 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).

Answer 1

(1)

Sample Size (n) is given by:

Given:

= 0.01

From Table, critical values of Z = 2.576

= 36.9

e = 4

Substituting, we get:

So,

Answer is:

565

(2)
SE = s/

= 3.4/

= 0.4761

= 0.02

ndf = n - 1 = 51 - 1 = 50

From Table, critical values of t = 2.4033

Confidence Interval:

16.6 (2.4033 X 0.4761)

= 16.6 1.1442

= ( 15.5 ,17.7)

Confidence Interval:

15.5 < <   17.7