As reported by B. Warner and J. Rutledge in the paper "Checking the Chips Ahoy! Guarantee" (Chance, Vol. 12, Issue 1, pp. 10-14), a random sample of forty-two 18-ounce bags of Chips Ahoy! cookies yielded a mean of 1261.6 chips per bag with a standard deviation of 117.6 chips per bag.
a. Determine a 95% confidence interval for the mean number of chips per bag for all 18-ounce bags of Chips Ahoy! cookies, and interpret your result in words.
b. Can you conclude that the average 18-ounce bag of Chips Ahoy! cookies contains at least 1000 chocolate chips? Explain your answer.