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You need to select a simple random sample of four from eight friends who will participate in a survey. Assume the friends are numbered \(1,2,3,4,5\), 6,7, and \(8 .\) Select four friends, using the two lines of numbers in the next column from a random number table. Read off each digit, skipping any digit not assigned to one of the friends. The sampling is without replacement, meaning that you cannot select the same person twice. Write down the numbers chosen. The first person is number 7 . $$ \begin{array}{lll} 07033 & 75250 & 34546 \\ \hline 75298 & 33893 & 64487 \end{array} $$ Which four friends are chosen?

You need to select a simple random sample of two from six friends who will participate in a survey. Assume the friends are numbered \(1,2,3,4,5\), and 6 . Use technology to select your random sample. Indicate what numbers you obtained and how you interpreted them. If technology is not available, use the line from a random number table that corresponds to the day of the month on which you were born. For example, if you were born on the fifth day of any month, you would use line \(05 .\) Show the digits in the line and explain how you interpreted them.

Assume your class has 30 students and you want a random sample of 10 of them. Describe how to randomly select 10 people from your class using the random number table.

Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a coin, and if the coin comes up heads, then he or she is in your sample. Explain why this is not a good method.

To determine if patrons are satisfied with performance quality, a theater surveys patrons at an evening performance by placing a paper survey inside their programs. All patrons receive a program as they enter the theater. Completed surveys are placed in boxes at the theater exits. On the evening of the survey, 500 patrons saw the performance. One hundred surveys were completed, and \(70 \%\) of these surveys indicated dissatisfaction with the performance. Should the theater conclude that patrons were dissatisfied with performance quality? Explain.

In carrying out a study of views on capital punishment, a student asked a question two ways: 1\. With persuasion: "My brother has been accused of murder and he is innocent. If he is found guilty, he might suffer capital punishment. Now do you support or oppose capital punishment?" 2\. Without persuasion: "Do you support or oppose capital punishment?" Here is a breakdown of her actual data. $$ \begin{aligned} &\text { Men }\\\ &\begin{array}{lcc} & \begin{array}{c} \text { With } \\ \text { persuasion } \end{array} & \begin{array}{c} \text { No } \\ \text { persuasion } \end{array} \\ \hline \text { For capital punishment } & 6 & 13 \\ \hline \text { Against capital punishment } & 9 & 2 \\ \text { Women } \end{array}\\\ &\begin{array}{lcc} & \begin{array}{c} \text { With } \\ \text { persuasion } \end{array} & \begin{array}{c} \text { No } \\ \text { persuasion } \end{array} \\ \hline \text { For capital punishment } & 2 & 5 \\ \hline \text { Against capital punishment } & 8 & 5 \end{array} \end{aligned} $$ a. What percentage of those persuaded against it support capital punishment? b. What percentage of those not persuaded against it support capital punishment? c. Compare the percentages in parts a and b. Is this what you expected? Explain.

a. If a rifleman's gunsight is adjusted incorrectly, he might shoot bullets consistently close to 2 feet left of the bull's-eye target. Draw a sketch of the target with the bullet holes. Does this show lack of precision or bias? b. Draw a second sketch of the target if the shots are both unbiased and precise (have little variation). The rifleman's aim is not perfect, so your sketches should show more than one bullet hole.

a. If a rifleman's gunsight is adjusted correctly, but he has shaky arms. the bullets might be scattered widely around the bull's-eye target. Draw a sketch of the target with the bullet holes. Does this show variation (lack of precision) or bias? b. Draw a second sketch of the target if the shots are unbiased and have precision (little variation). The rifleman's aim is not perfect, so your sketches should show more than one bullet hole.

Suppose that, when taking a random sample of three students' GPAs, you get a sample mean of \(3.90 .\) This sample mean is far higher than the collegewide (population) mean. Does that prove that your sample is biased? Explain. What else could have caused this high mean?

Suppose you attend a school that offers both traditional courses and online courses. You want to know the average age of all the students. You walk around campus asking those students that you meet how old they are. Would this result in an unbiased sample?