In #1-2, state whether you think a sample or the entire population should be studied. Explain why.
1) A manufacturer is planning on selling padded headrests at an airport for travelers to purchase and use on planes. They need to determine if the headrest is comfortable enough.
2) You are having a party for the people at your workplace. You need to determine how many people are going to attend in order to plan for the party.
In #3-4, identify the population being studied. Why should only a sample be studied in each example?
3) A medical research group wants to study the impact of soda consumption on children's physical activity in the United States.
4) You are interested in the favorite color of students at Naperville Central. You decide to conduct a survey to determine the color preference of students.
In #5-6, explain why the sample obtained may be biased.
5) You are interested in what type of concessions people purchase the most at an MLB game. You decide to set up a stand and offer your survey to people as they walk by.
6) You are interested in learning what percentage of people in Naperville pay for cable television. You decide to talk to the Naperville Sun and they agree to send out a survey card with their newspaper for one week. You put a return address on each card so people can send their responses back to you.
In #7-11, identify the type of sampling method used.
7) Apple selects every 100th cell phone from the assembly line for careful testing and analysis.
8) The principal at NNHS interviews 5 students from each 3rd period class.
9) The CEO of a fortune 500 company wants to gauge employee morale. He picks \(10\) women and \(10\) men from each department and interviews them.
10) A coach writes the name of all athletes on the varsity football team in a hat and draws names at random.
11) Netflix sends out a questionnaire via email to each of its subscribers and analyzes the responses.
Review
12) Let \(f(x)=2x-3\) and \(g(x)= 5x^2-1\), determine \(g(f(x))\) in standard polynomial form.
13) The half life of a substance is \(15\) hours. Determine how long it will take for a sample to deteriorate to \(\frac{1}{10}\) of its initial amount.
14) Prove that \(S_n=\sum\limits_{i=1}^{n} r^{i-1} = \frac{1-r^n}{1-r}\) when \(0<r<1\).
15) Use the formula from #14 to make an argument as to why \(\sum\limits_{i=1}^{\infty} r^{i-1} = \frac{1}{1-r}\) if and only if \(|r|<1\).
Solution Bank
1) A manufacturer is planning on selling padded headrests at an airport for travelers to purchase and use on planes. They need to determine if the headrest is comfortable enough.
2) You are having a party for the people at your workplace. You need to determine how many people are going to attend in order to plan for the party.
In #3-4, identify the population being studied. Why should only a sample be studied in each example?
3) A medical research group wants to study the impact of soda consumption on children's physical activity in the United States.
4) You are interested in the favorite color of students at Naperville Central. You decide to conduct a survey to determine the color preference of students.
In #5-6, explain why the sample obtained may be biased.
5) You are interested in what type of concessions people purchase the most at an MLB game. You decide to set up a stand and offer your survey to people as they walk by.
6) You are interested in learning what percentage of people in Naperville pay for cable television. You decide to talk to the Naperville Sun and they agree to send out a survey card with their newspaper for one week. You put a return address on each card so people can send their responses back to you.
In #7-11, identify the type of sampling method used.
7) Apple selects every 100th cell phone from the assembly line for careful testing and analysis.
8) The principal at NNHS interviews 5 students from each 3rd period class.
9) The CEO of a fortune 500 company wants to gauge employee morale. He picks \(10\) women and \(10\) men from each department and interviews them.
10) A coach writes the name of all athletes on the varsity football team in a hat and draws names at random.
11) Netflix sends out a questionnaire via email to each of its subscribers and analyzes the responses.
Review
12) Let \(f(x)=2x-3\) and \(g(x)= 5x^2-1\), determine \(g(f(x))\) in standard polynomial form.
13) The half life of a substance is \(15\) hours. Determine how long it will take for a sample to deteriorate to \(\frac{1}{10}\) of its initial amount.
14) Prove that \(S_n=\sum\limits_{i=1}^{n} r^{i-1} = \frac{1-r^n}{1-r}\) when \(0<r<1\).
15) Use the formula from #14 to make an argument as to why \(\sum\limits_{i=1}^{\infty} r^{i-1} = \frac{1}{1-r}\) if and only if \(|r|<1\).
Solution Bank