Each sampling method suffers from a form of bias. Identify the bias, tell how the sample statistic might deffer significantly from the population parameter, and suggest how the problem might be corrected. To gather feedback on his teaching, Professor Jones invites his students to visit his Web site and respond to a brief questionnaire. He is depressed to discover that 68% of those who respond are dissatisfied with his teaching.

How often are “fresh wild salmon” really farm-bred? Newspaper reporters visited eight stores in New York City and bought samples of salmon sold as “wild” to a laboratory. The results showed that 6 of the 8 samples were actually farm-bred, based on analysis of pigments known as carotenoids. What kind of sampling method would you suppose was used? (See The NewYork Times, April 10, 2005.)

Identify any possible sources of bias in the sampling pro- cedure in the following scenario.

A soft-drink company produces a lemon-lime drink that it says people prefer by a margin of two-to-one over its main competitor, a cola. To prove this claim, it sets up a booth in a large shopping mall where customers are allowed to try both drinks. The customers are filmed for a possible television commercial. They are asked which drink they prefer.

Tell whether the sampling strategy will result in a random sample from the population under consideration. If it is not random, explain why it is not. To get a sample of 50 students for a student services survey, an assistant principal uses the calculator command "randInt $(1,72,5)$ " to pick five numbers between 1 and 72 . He goes to those five pages in the 72-page student directory and chooses the ten students pictured on each of those five pages.

Newspaper readers sometimes write letters to the editor, hoping that their opinions will be published in the paper. The editorial staff at a local newspaper keeps track of the content of each letter that is submitted. After a controversial decision made by the mayor, 90% of the letters to the editor expressed opposition to the mayor's action. Explain why this sampling method is biased. Is 90% likely greater than or less than the percentage of all citizens who oppose the mayor's action?

Karla, a senior at Springfield High School, wants to estimate the mean number of Facebook friends that students at the school have. To gather data, she makes an announcement one morning on the school's P.A. system asking students to find her during the 12th-grade lunch period and report the number of Facebook friends they have on a slip of paper. Describe an unbiased sampling method that Karla could use to obtain a better estimate.

Given the recent economic downturn, only $60 \%$ in a graduating class of 250 will find employment in the first round of a job search. You have 20 friends who have recently graduated.

a. Discuss the sampling distribution of the sample proportion of your friends who will find employment in the first round of a job search.

b. What is the probability that less than $50 \%$ of your friends will find employment in the first round of a job search?

To estimate the population in a rookery, 4965 fur seal pups were captured and tagged in early August, In late August 900 fur seal pups were captured. Of these, 218 had Seen tagged. Based on these figures, estimate the population of fur seal pups in the rookery. [Source: Chapman and Johnson, "Estimation of Fur Seal Pup Populations by Randomized Sampling," Transactions of the American Fisheries Society, 97 (July 1968), 264-270.]

Suppose that we will randomly select a sample of $64$ measurements from a population having a mean equal to $20$ and a standard deviation equal to $4.$

Calculate the probability that we will obtain a sample mean greater than $21$; that is, calculate $P(\overline{x} > 21)$. Hint: Find the $z$ value corresponding to $21$ by using $\mu_{\overline{x}}$ and $\sigma_{\overline{x}}$ because we wish to calculate a probability about $\overline{x}$. Then sketch the sampling distribution and the probability.

The director of the Glee Club would like to know if her Booster Club parents would do a fundraiser. Which sampling method is most likely to yield an accurate prediction of the population?

A Survey every 3rd Booster Club parent who comes to a fundraiser meeting.

B Survey every 10th Booster Club parent who comes to a fundraiser meeting.

C Survey only the parents who respond to a letter from the director.

Multiple choice: What's a simple random sample?

A simple random sample of size n is one in which

a. Every n-th member is selected from the population.

b. Each possible sample of size n has the same chance of being selected.

c. There is exactly the same proportion of women in the sample as is in the population.

d. You keep sampling until you have a fixed number of people having various characteristics (e.g., males, females).

The Gallup Poll interviewed 1022 randomly selected U.S. adults aged 18 and older, March 7-10, 2013. Gallup reports that when asked whether respondents thought that global warming was due primarily to human activities, $57 \%$ of respondents said it was. If you can't tell, then say so-this often happens when we read about a survey.

e) The sampling method, including whether or not randomization was employed

In an observational study at Turner Field in Atlanta, Georgia, 43 percent of the men were observed not washing their hands after going to the bathroom (Source: Harris Interactive). Assume that this percentage is true for the current population of U.S. men. Let $\hat{p}$ be the proportion in a random sample of 110 U.S. men who do not wash their hands after going to the bathroom. Find the mean and standard deviation of the sampling distribution of $\hat{p}$, and describe its shape.

The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples of size 25 are drawn from this population and the means recorded to the nearest tenth of a centimeter. Determine (a) the mean and standard deviation of the sampling distribution of $\hat{X}$ ; (b) the number of sample means that fall between 172.5 and 175.8 centimeters inclusive; (c) the number of sample means falling below 172.0 centimeters.