The quality-control department at an automobile factory checks the tightness of motor-mounting bolts installed by assembly-line workers by sampling the first 25 cars produced by the assembly line each day. Explain why this sampling method is biased. Is this method likely to overestimate or underestimate the proportion of bolts that are improperly tightened?

TV commentator Lou Dobbs doesn't like illegal immigration. One of his shows was largely devoted to attacking a proposal to offer driver's licenses to illegal immigrants. During the show, Dobbs invited his viewers to loudobbs.com to vote on the question "Would you be more or less likely to vote for a presidential candidate who supports giving driver's licenses to illegal aliens?" The result: 97% of the 7350 people who voted by the end of the show said, "Less likely." Explain why this sampling method is biased. Is 97% likely greater than or less than the percentage of all Americans who would say "Less likely"?

You are on the staff of a member of Congress who is considering a bill that would provide government-sponsored insurance for nursing-home care. You report that 1128 letters have been received on the issue, of which 871 oppose the legislation. "I'm surprised that most of my constituents oppose the bill. I thought it would be quite popular," says the congresswoman. Are you convinced that a majority of the voters oppose the bill? How would you explain the statistical issue to the congresswoman?

Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would be more effective for patients who had already had a stroke. Here are the data on strokes during the two years of the study:

$$\begin{array}{clcc} \hline & & \text { Number of } & \text { Number who had } \\ \text { Group } & \text { Treatment } & \text { patients } & \text { a stroke } \\ \hline 1 & \text { Placebo } & 1649 & 250 \\ 2 & \text { Aspirin } & 1649 & 206 \\ 3 & \text { Dipyridamole } & 1654 & 211 \\ 4 & \text { Both } & 1650 & 157 \\ \hline \end{array}$$

Summarize these data in a two-way table.

The article “Application of Surgical Navigation to Total Hip Arthroplasty” reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. a. Find a 95% confidence interval for the mean surgery time for this procedure. b. Find a 99.5% confidence interval for the mean surgery time for this procedure. c. A surgeon claims that the mean surgery time is between 133.9 and 139.9 minutes. With what level of confidence can this statement be made? d. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within $\pm 3$ minutes? e. Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within $\pm 3$ minutes?

Find the mean of the data given. Number of apps on five friends' smart phones: 42,42,23,75,64

A radio station is giving away free t-shirts to students in local schools. It plans to give away 40 shirts at Big Sky Middle School and 75 shirts at High Peaks High School. Big Sky Middle School has 350 students, and 800 students attend High Peaks High School. a. What is the probability of getting at-shirt if you are a student at the middle school? b. What is the probability of getting at-shirt if you are a student at the high school? c. Are you more likely to get at-shirt if you are a student at the high school, or at the middle school?

You have probably seen the mall interviewer, approaching people passing by with clipboard in hand. Explain why even a large sample of mall shoppers would not provide a trustworthy estimate of the current unemployment rate.

How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student surveyed the first 100 students to arrive at school on a particular morning. These students reported an average of 7.2 hours of sleep on the previous night. Explain why this sampling method is biased. Is 7.2 hours probably higher or lower than the true average amount of sleep last night for all students at the school? Why?

A forester studying the woolly adelgid, an invasive species of insect that infests and weakens hemlock trees, wants to estimate the proportion of hemlocks in a large forest that are infested. He starts at a roadside rest area and walks along the road, using the first 50 hemlocks he encounters as his sample. He finds that 72% of the trees are infested by the woolly adelgid. Explain why this sampling method is biased. Is 72% likely to be greater than or less than the percent of all hemlock trees in the forest that are infested?

A forester studying the woolly adelgid, an invasive species of insect that infests and weakens hemlock trees, wants to estimate the proportion of hemlocks in a large forest that are infested. He starts at a roadside rest area and walks along the road, using the first 50 hemlocks he encounters as his sample. He finds that 72% of the trees are infested by the woolly adelgid. What type of sample did the forester obtain?

In the EAI sampling problem, the population mean is $51,100 and the population standard deviation is$5,000. When the sample size is n = 30, there is a 0.489 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

An educator wants to compare the effectiveness of computer software for teaching biology with that of a textbook presentation. She gives a biology pretest to each of a group of high school juniors, then randomly divides them into two groups. One group uses the computer, and the other studies the text. At the end of the year, she tests all the students again and compares the increase in biology test scores in the two groups. Is this an observational study or an experiment? Justify your answer.

How much vitamin C does orange juice contain? A nutrition magazine measures the amount of vitamin C in 50 half-gallon containers of a popular brand of orange juice from 10 different grocery stores and concludes that the containers produced by this company do not have as much vitamin C as advertised. Identify the population and sample in this setting.