The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor of the prison project. What can the city council conclude about public support for the mayor's initiative?

What were four of the trading city-states that arose along the East African coast?

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, $58 \%$ were winners.

b) If there are 100 students in the class, are you surprised that one was this successful? Explain.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, $58 \%$ were winners.

a) What do you think of his claim? Explain.

Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, ... , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

$$\begin{matrix} \text{0} & \text{0} & \text{34} & \text{34} & \text{34} & \text{45} & \text{41} & \text{51} & \text{55} & \text{36} & \text{47} & \text{41} & \text{0} & \text{0} & \text{53} & \text{54} & \text{38} & \text{0} & \text{41} & \text{47}\\ \end{matrix}$$

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

b) Where do you wish the histogram to be centered?

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

d) Describe why a Normal model should not be used here.

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 1000 people randomly selected from their mailing list of over 200,000 people. They get orders from 123 of the recipients.

Create a 90% confidence interval for the percentage of people the company contacts who may buy something.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

b) Confirm that you can use a Normal model here.

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Assume a company wants to test the response to a new flyer and sends it to 1000 people randomly chosen from their mailing list of over 200,000 people. They get orders from 123 of the recipients.

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? Describe.

Direct mail advertisers send solicitations ("junk mail") to thousands of potential customers in the hope that some will buy the company's product. The response rate is usually quite low. Assume a company wants to test the response to a new flyer and sends it to 1000 people randomly chosen from their mailing list of over 200,000 people. They get orders from 123 of the recipients.

c) Describe what " $90 \%$ confidence" means.

Consider each situation described. Identify the population and the sample, explain what p and

$$\hat { p }$$

represent, and tell whether the methods of this chapter can be used to create a confidence interval. A consumer group hoping to assess customer experiences with auto dealers surveys 167 people who recently bought new cars; 3% of them expressed dissatisfaction with the salesperson.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

d) There is a $48 \%$ chance that a randomly chosen coworker has received the vaccine.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$, and you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$.

a) How would the confidence interval change if the sample size had been 800 instead of 200?