Question

aren 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 9.1 and a standard deviation of 2.2. What is the 95% confidence interval for the number of chocolate chips per cookie for Big Chip cookies

Answer 1

The 95% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is between 4.68 and 13.52.

Explanation:

We have the standard deviation of the sample, so we use the students' t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 51 - 1 = 50

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 50 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975([tex]t_(975)`). So we have T = 2.01

The margin of error is:

M = T*s = 2.01*2.2 = 4.42

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.1 - 4.42 = 4.68

The upper end of the interval is the sample mean added to M. So it is 9.1 + 4.42 = 13.52

The 95% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is between 4.68 and 13.52.