Question

The data on the number of chocolate chips per bag for 42 bags of Chips Ahoy! cookies were obtained by the students in an introductory statistics class at the United States Air Force Academy in response to the Chips Ahoy! 1,000 Chips Challenge sponsored by Nabisco, the makers of Chips Ahoy! Use the data collected by the students to answer the following questions and to conduct the analyses required in each part. They found ¯xx¯ = 1261.6 and s = 117.6

a. Determine a 95% confidence interval for the mean number of chips per bag for all bags of Chips Ahoy! cookies.

≤μ≤≤μ≤

b. Interpret your result in words.

c. Can you conclude that the average bag of Chips Ahoy! Cookies contain at least 1000 chocolate chips?

• yes
• no

d. Explain why or why not.

Answer 1

n=42, =1261.6, s=117.6, C=95%=0.95

a)

Formula for confidence interval is

Where tc is the t critical value for C= 0.95

with df = n-1 = 42 - 1 = 41

we get t critical value as

tc = 2.02

1224.944 < < 1298.255

1224.94 < < 1298.26

b) Therefore we are 95% confident that the true mean number of chips per bag for all bags of Chips Ahoy! cookies lies between  1224.944 to 1298.255.

c) Yes,

d) because 1000 is less than the range of our confidence interval.