Exam 14: Sampling and Simulation

A pollster wants to determine which local news channel is watched most frequently in New York City. Two city blocks in Manhattan are used as a sample. What type of sampling technique is being used?

"What are your three favorite flavors of ice cream?" would be an example of which type of question?

Sampling techniques are often used

What type of question gives the subject a list of possible responses from which to choose?

A sample is said to be ______________ if it is a randomly chosen representation of the population.

A researcher is using a random numbers table to pick between two groups labeled X and Y. X is to be chosen with probability 5/7 and Y with probability 2/7. The researcher assigns the digits 1, 2, 3, 4, and 5 to X, and she assigns the digits 6 and 7 to Y. The remaining digits are neglected. The researcher uses this section of a random number table 6 8 5 1 7 4 4 0 4 0 What are the first and second choices?

A statistics teacher taught Introductory Statistics to a large lecture class of 200 students. She wanted to estimate the average on the first examination by selecting every eighth student's test score and finding the average of these scores. What type of sampling technique is being employed?

Samples are said to be biased when some type of systematic error has been made in the selection of the subjects.

A researcher wants to learn about unemployment rates across the country. She takes an alphabetical list of the 50 states, numbers the states in order, and selects one state at random. She surveys that state and every every tenth state after it, cycling through the list. What type of sampling technique is the researcher employing?

In simulating experiments using the Monte Carlo method, one must define a correspondence between the random numbers and the outcomes.

One major disadvantage of cluster sampling is that the elements in a cluster may not have the same variation in characteristics as elements selected individually from a population.

A new product is being introduced, and a nationwide survey to determine the public's opinion of the product is to be conducted. The country is divided into six regions, then two states are randomly selected from each region, and then each state is divided into rural and urban markets. A number of these markets are selected, and randomly selected people is these markets are surveyed about the new product. What type of sampling technique is being employed here?

For a sample to be _______________, every member of the population must have an equal chance of being selected.

The basic simulation technique using random numbers is referred to as the Las Vegas method.

A bin at the store is filled with T-shirts. They are all sized either small or large, and there are approximately equal numbers of each, so the chance of picking either size is 0.5. You need to buy four T-shirts for your friends, all wear small. You want to know how many shirts you must pull out of the bin before you have at least four smalls. Use the random numbers table below to simulate your T-shirt selections. The highlighted numbers were randomly chosen and serve as the first selections for the different trials. Repeat the simulation five times, beginning each trial at a different highlighted number. Work down the columns, and move from left to right, column to column as needed. Let the even digits correspond to selecting a small, and the odd digits correspond to selecting a large. What is the greatest number of shirts your experiments indicate you need to pull out of the bin before you have four smalls?

In a free-throw relay, one member of a team of four shoots free-throws (a type of shot in basketball) until she makes one, then the next team member shoots until she makes one. This continues through the third and forth team members. In a competition, the first team to finish wins. The question arises whether it is better to have four average shooters or two good shooters and two not-so-good ones, if the overall shooting percentage of the teams is the same. Use a Monte Carlo simulation to help answer this question. Each number in the random numbers table below will correspond to one free throw. One simulated team has four 50% free-throw shooters (the 50's). The order of the shooters does not matter. The digits 0-4 will correspond to making a free throw and the digits 5-9 will correspond to missing. The other simulated team has two 80% free-throw shooters and two 20% free-throw shooters (the 80/20's). Let the 80% shooters be the first two of the four to shoot. For the 80% shooters, the digits 0-7 will correspond to making the free throw, and the digits 8-9 will correspond to missing. For the 20% shooters, the digits 0-1 will correspond to making the free throw and 2-9 will correspond to missing. Work down the columns, moving to the column to the right as needed. The highlighted numbers were selected at random. Begin the 80/20's team at the 6, and begin the 50's team at the 7. Simulate one race for each team. Count the number of shots each team needs to finish.

In multistage sampling, a very large population is given a questionnaire to determine those who meet the qualifications for the study.

A researcher is using Monte Carlo techniques to simulate wins and losses in a particular game. When the number 1, 2, or 3 appears, player A is the winner. When the number 4, 5, or 6 appears, player B is the winner. If the number 7, 8, 9, or 0 appears, the game is a draw. Given the following sequence of randomly generated numbers, how many games did player A win? 4, 5, 8, 5, 9, 3, 6, 4, 5, 1, 8, 3, 6