AP STATS 4.1

A stratified random sample addresses the same issues as which of the following experimental designs?

A block design.

Simple random sampling

None of the above.

A candidate for mayor of Dallas wants to know what proportion of city residents support his candidacy. His staff calls 1,000 people chosen at random from the city telephone directory; 850 of them respond. What are the population and the sample in this example?

Population: all Dallas residents. Sample: the 850 people who respond

A stratified random sample is appropriate when

The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is very similar within the groups but quite different between groups.

A poll conducted by the student newspaper asked, "Who do you believe will win the Ohio State Undergraduate Student Government elections?" In order to vote, one had to access the student newspaper's Web site and record one's vote. The results of the poll were summarized in a graphic similar to the following. Which of the following statements is true about these results?

The results of the survey are unreliable because response to the survey was voluntary.

Use Scenario 4-1. The newspaper asks you to comment on their survey of local opinion. You say:

This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents.

In order to assess the opinion of students at the University of Minnesota on campus snow removal, a reporter for the student newspaper interviews the first 12 students he meets who are willing to express their opinion. The method of sampling used is

a convenience sample

A simple random sample of size n is defined to be

a sample of size n chosen in such a way that every set of n units in the population has an equal chance to be the sample actually selected

A simple random sample is

a sample that gives every possible sample of the same size the same chance to be selected.

A news release for a diet products company reports: "There's good news for the 65 million Americans currently on a diet." Its study showed that people who lose weight can keep it off. The sample was twenty graduates of the company's program who endorse it in commercials. The results of the study are probably

biased, overstating the effectiveness of the diet.

A study sponsored by American Express Co. and the French government tourist office found that old stereotypes about French unfriendliness were not true. The respondents were more than 1000 Americans who have visited France more than once for pleasure over the past two years. The results of this study are probably

biased, overstating the extent to which the old stereotypes were not true.

To determine the proportion of each color of Peanut Butter M&M, you buy 10 1.69 ounce packages and count how many there are of each color. This is an example of

cluster sampling

A marine biologist wants to estimate the mean size of the barnacle Semibalanus balnoides on a stretch of rocky shoreline. To do so, he randomly selected twenty 10-cm. square plots and measured the size of every barnacle in each plot. This is an example of

cluster sampling.

Does caffeine improve exam performance? Suppose all students in the 8:30 section of a course are given a "treatment" (two cups of coffee) and all students in the 9:30 section are not permitted to have any caffeine before a mid-term exam. Use Scenario 4-6. Unfortunately, any systematic difference between the two sections on the exam might be due to the fact that the 8:30 and 9:30 classes have different instructors. This is an example of

confounding

An opinion research firm wants to find the country's reaction to a speech by a famous politician. They randomly select six states, then randomly select ten Zip Codes from each state. Fifty people from each Zip Code are randomly selected for the survey. This is an example of

multistage sampling

In order to select a sample of undergraduate students in the United States, I select a simple random sample of four states. From each of these states, I select a simple random sample of two colleges or universities. Finally, from each of these eight colleges or universities, I select a simple random sample of 20 undergraduates. My final sample consists of 160 undergraduates. This is an example of

multistage sampling

In an experiment, an observed effect so large that it would rarely occur by chance is called

statistically significant

A public opinion poll in Ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a

stratified random sample

You plan to give a math achievement test to samples of 15 year-olds from both the U.S. and Korea in order to compare mathematics knowledge in the two countries. In each country, you will randomly choose 300 students from low-income families 400 students from middle-income families 200 students from high-income families The sample from Korea is a

stratified random sample.

We divide the class into two groups: first year students and others. We then take random samples from each group. This is an example of

stratified random sampling

Use Scenario 4-2. The sample is

the 1347 teachers who mail back the questionnaire

Use Scenario 4-1. The sample for the survey is

the 20 people who gave the sportswriter their opinion.

Use Scenario 4-6. Instead of giving all students in the 8:30 section two cups of coffee, students in the 8:30 section are randomly assigned to a treatment group (two cups of coffee) or a control group (two cups of decaffeinated coffee). The coffee is so bad that students cannot tell whether they are in the treatment or the control group. As it turns out, students in both groups do better on the exam than students in the 9:30 section, who weren't given anything. This could be the result of

the placebo effect.

A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. The chance that all 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses selected is

the same as for any other set of 100 residential addresses.

A television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. Of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. The viewers who phoned in are

a voluntary response sample.

You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. In all 1347 teachers return the questionnaire. Use Scenario 4-2. The population is

all American school teachers.

A sportswriter wants to know how strongly Lafayette residents support the local minor league baseball team, the Lafayette Leopards. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium. Use Scenario 4-1. The intended population for this survey is

all residents of Lafayette.