Problem 1, Chips Ahoy [3 points]
In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips
Challenge,” claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at
least 1000 chocolate chips. Dedicated statistics students at the Air Force Academy (no
kidding) purchased some randomly selected bags of cookies and counted the chocolate
chips. Some of their data are given below.
1219 1214 1087 1200 1419 1121 1325 1345
1244 1258 1356 1132 1191 1270 1295 1135
(a) Check the assumptions and conditions for inference. Comment on any concerns you
have.
(b) Create a 90% confidence interval for the average number of chips in bags of Chips
Ahoy! cookies.
(c) What does this confidence interval say about Nabisco’s claim?
Problem 2, Populations and samples [4 points]
Conditions For each situation described below, identify the population and the sample,
explain what p and pb represent, and tell whether the methods of this chapter can be
used to create a confidence interval.
(a) Police set up an auto checkpoint at which drivers are stopped and their cars in-
spected for safety problems. They find that 13 of the 131 cars stopped have at least
one safety violation. They want to estimate the percentage of all cars that may be
unsafe.
(b) A TV talk show asks viewers to register their opinions on prayer in schools by logging
on to a website. Of the 598 people who voted, 481 favored prayer in schools. We
want to estimate the level of support among the general public.
(c) A school is considering requiring students to wear uniforms. The PTA surveys
parent opinion by sending a questionnaire home with all 1255 students; 390 surveys
are returned, with 238 families in favor of the change.
(d) A college admits 1650 freshmen one year, and four years later, 1375 of them graduate
on time. The college wants to estimate the percentage of all their freshman enrollees
who graduate on time.

Problem 3, Internet orders [5 points]
A catalog sales company promises to deliver orders placed on the Internet within 3 days.
Follow-up calls to a few randomly selected customers show that a 95% confidence interval
for the proportion of all orders that arrive on time is 86% ± 6%. What does this mean?
Are these conclusions correct? Explain.
(a) Between 80% and 92% of all orders arrive on time.
(b) Ninety-five percent of all random samples of customers will show that 86% of orders
arrive on time.

(c) Ninety-five percent of all random samples of customers will show that 80% to 92%
of orders arrive on time.
(d) We are 95% sure that between 80% and 92% of the orders placed by the sampled
customers arrived on time.
(e) On 95% of the days, between 80% and 92% of the orders will arrive on time.
Problem 4, Confidence interval statements [4 points]
Several factors are involved in the creation of a confidence interval. Among them are
the sample size, the level of confidence, and the margin of error. Which statements are
true?
(a) For a given sample size, higher confidence means a smaller margin of error.
(b) For a specified confidence level, larger samples provide smaller margins of error.
(c) For a fixed margin of error, larger samples provide greater confidence.
(d) For a given confidence level, halving the margin of error requires a sample twice as
large.
Problem 5, Direct advertising [4 points]
Direct mail advertisers send solicitations (a.k.a. “junk mail”) to thousands of potential
customers in the hope that some will buy the company’s product. The acceptance rate
is usually quite low. Suppose a company wants to test the response to a new flyer, and
sends it to 1024 people randomly selected from their mailing list of over 200,000 people.
They get orders from 130 of the recipients.
(a) Create a 90% confidence interval for the percentage of people the company contacts
who may buy something.
(b) Explain what this interval means.
(c) Explain what “90% confidence” means.
(d) The company must decide whether to now do a mass mailing. The mailing won’t
be cost-effective unless it produces at least a 5% return. What does your confidence
interval suggest? Explain
Problem 6, Automobile emissions [2 points]
A state’s environmental agency worries that many cars may be violating clean air emis-
sions standards. The agency hopes to check a sample of vehicles in order to estimate
that percentage with a margin of error of 3% and 90% confidence. To gauge the size of
the problem, the agency first picks 70 cars and finds 8 with faulty emissions systems.
How many should be sampled for a full investigation?