Exam 14: Sampling and Simulation

Five-digit random numbers are used to simulate scores on each hole in an 18-hole round c The correspondence between the random numbers and scores on each hole is chosen to bc follows. Numbers Score (Probability) 00000 Hole-in-one (0.001\%) 00001-05000 Eagle (5\%) 05001-20000 Birdie (15\%) 20001-60000 Par (40\%) 60001-90000 Bogey (30\%) 90001-99999 Double-Bogey (10\%) Use the following portion of a random numbers table starting with the highlighted numbe and determine how many holes the simulated golfer made par or better (i.e., how many holes-in-one, eagles, birdies, and pars were obtained in the 18 holes). Use the highlightec as the score on the first hole; work down a column moving from left to right, column to $\mathrm { c }$ : needed. olf. number Lumn as

The survey question "Do you feel that, if people were not allowed to park along this street, that children would not be able to play there?" is a poor survey question because it

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 7 9 2 1 5 7 7 3 1 1 What are the first and second choices?

Why would researchers want to use a simulation rather than study the actual situation?

The PAC-10 Conference consists of ten schools. Schools of the PAC-10 1 - Arizona 5 - Oregon State 9 - Washington 2 - Arizona State 6 - Stanford 0 - Washington State 3 - California 7 - UCLA 4 - Oregon 8 - USC Use systematic sampling selecting every second number from the population to identify five schools out of the ten as a sample. The following random numbers table has already been used to randomly select the first school, Arizona State. What are the other four schools in the sample? 1 0 4 8 0 2 2 3 6 8 2 4 1 3 0 4 2 1 6 7 3 7 5 7 0 7 7 9 2 1 9 9 5 6 2 9 6 2 0 1 8 9 5 7 9 8 5 2 7 5 2 8 9 1 8 6 3 2 5 3 0 9 4 2 9 1 0 3 6 5 1 0 3 6 5 0 7 2 1 9 5 1 0 8 5 0 2 3 6 8 0 1 0 1 1 5 2 1 6 2

If a third of a population is female, then approximately a third of the representative sample should be female.

Sampling methods often use random numbers to select samples.

In many women's tennis matches they play best-out-of-three sets. In other words, they play until one player wins two sets, and there are no ties. Lourdes and Mariana are two rivals, though Lourdes seems to win about six sets for every four that Mariana wins. Use the random numbers table below to simulate 10 matches between Lourdes and Marian. Let an entry in the table correspond to one set, 0-5 corresponds to Lourdes winning the se corresponds to Mariana winning the set. Begin each match with a different highlighted $\mathrm { nl }$ and use it with up to two entries below it to represent a match. In how many of the ten simulated matches needed all three sets?

A flip of a fair coin is used to simulate the gender of a series of simulated students. Flip Gender Female Male Given the following four flips, how many male students were there?

A pollster wanted to determine how much support a new library tax would have in a major metropolitan area. The metro area is divided into regions, Southeast, Southwest, Northeast, Northwest, and Central and 100 voters in each region are surveyed. What type Of sampling technique is being employed?

Which of the following is not a valid advantage for studying a sample rather than an entire population?

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

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

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

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, three larges and one small. You want to know how many shirts you must pull out of the bin before you have at least three larges and one small. Use the random numbers table below to simulate your $\mathrm { T }$ -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 select a large. Number Size 0,2,4,6,8 Small 1,3,5,7,9 Large What is the greatest number of shirts your experiments indicate you need to pull out of thı before you have three larges and one small? e bin

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?

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 the same. Use a Monte Carlo simulation to help answer this question. Each number in th 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 shooter not matter. The digits 0-4 will correspond to making a free throw and the digits $5 - 9$ will correspond to missing. does mbers The other simulated team has two $80 \%$ free-throw shooters and two $20 \%$ free-throw shoo $80 / 20$ '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 1 were selected at random. Begin the $80 / 20$ 's team at the 6 , and begin the 50 's team at the 7 (the Simulate one race for each team. Count the number of shots each team needs to finish.

A small-town politician is running for the district council seat. If the politician decides to poll three blocks in the district to determine his chance of winning the seat, what type Of sampling is being used?

Five students were scheduled to take a five-question true-false quiz on the history of the Peloponnesian War. Since they didn't know anything about the subject, they were faced with a decision of whether or not to study. Before they decided to study they decided to run a simulation to see how many of them would likely pass the quiz if they all just guessed randomly. At least three correct answers would be needed to pass. They made uf hypothetical set of correct answers as shown in the following table. Question Correct Answer 1 2 3 4 5 They then used the following random numbers table to ensure that the simulated response be truly random. Each simulated set of quiz responses began with a different highlighted from the table and included the four numbers beneath it. An odd number was said to corr an answer of True, and an even number was said to correspond to an answer of False. How many passing grades were there in the five simulated responses? number pond to

Which of the following is not an advantage of cluster sampling over the other sampling techniques?