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Chapter 1: Problem 6

A coach must select two players to serve as captains. He wants to randomly select two players to be the captains. Obtain a simple random sample of size 2 from the following list: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn. Write a short description of the process you used to generate your sample.

Short Answer

Expert verified
Assign numbers to the players and use a random number generator to select two.

Step by step solution

01

- List the Players

Start by listing the names of all the players: Mady, Breanne, Evin, Tori, Emily, Clair, Caty, Jory, Payton, Jordyn.
02

- Assign Numbers

Assign a unique number to each player: 1. Mady, 2. Breanne, 3. Evin, 4. Tori, 5. Emily, 6. Clair, 7. Caty, 8. Jory, 9. Payton, 10. Jordyn.
03

- Randomly Select Two Numbers

Use a random number generator to select two unique numbers between 1 and 10. These numbers correspond to the players.
04

- Match Numbers to Players

Find the players that correspond to the randomly selected numbers from Step 3. These will be the selected captains.
05

- Write the Selected Captains

Based on the randomly selected numbers, write down the names of the two players selected as captains.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simple Random Sample
A Simple Random Sample (SRS) is a basic type of random sampling where every member of the population has an equal chance of being selected. When the coach wants to randomly select two captains from a group of players, using an SRS ensures fairness. Here鈥檚 how it works:
  • Each player must have an equal opportunity to be chosen.
  • The selection process does not favor any player over another.
This method is essential because it maintains unbiased selection, leading to representative results. In real-life scenarios, such methods ensure transparency and accuracy.
Random Number Generator
A Random Number Generator (RNG) is a tool used to produce random numbers. These numbers are crucial for ensuring the randomness in sampling. In the exercise, the coach uses an RNG to choose the captains. Here鈥檚 a simple way to use an RNG:
  • Assign a number to each player (e.g., 1 to 10).
  • Input the range (1-10) into the generator.
  • Generate the numbers without any bias or pattern.
By using a RNG, the coach ensures that the selection is random, further maintaining the integrity of the Simple Random Sample.
Selection Process
The selection process in random sampling involves several steps to ensure fairness and transparency. In our example, the coach must follow these steps:
  • List all players and assign each a unique number.
  • Use the RNG to pick two random numbers.
  • Select the players corresponding to these numbers.
This structured approach avoids biases and ensures that each player has a fair shot at being chosen. Thus, a properly executed selection process is key to maintaining random sampling鈥檚 integrity.
Probability
Probability is the likelihood of an event happening. In random sampling, it鈥檚 the chance of any one individual being chosen. Here, each of the 10 players has a 1 in 10 chance (or 10%) of being selected as a captain. Understanding probability helps in realizing how random sampling works. Key points about probability in this context:
  • Each player starts with an equal probability.
  • The use of RNG prevents changes in these probabilities.
  • Probability in random sampling ensures fair and unbiased selection.
Ensuring that these probabilities remain equal is vital for the accuracy and fairness of the sampling process.

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Most popular questions from this chapter

Consider the following two questions: (a) Do you believe that the government should or should not be allowed to prohibit individuals from expressing their religious beliefs at their place of employment? (b) Do you believe that the government should or should not be allowed to prohibit teachers from expressing their religious beliefs in public school classrooms? Do you think the order in which the questions are asked will affect the survey results? If so, what can the pollster do to alleviate this response bias? Discuss the choice of the word prohibit in the survey questions.

In Problems 11-22, identify the type of sampling used. The city of Naperville is considering the construction of a new commuter rail station. The city wishes to survey the residents of the city to obtain their opinion regarding the use of tax dollars for this purpose. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

Determine the level of measurement of each variable. Assessed value of a house

Are young couples who marry or cohabitate more likely to gain weight than those who stay single? Researchers followed 8000 men and women for 7 years. At the start of the study, none of the participants were married or living with a romantic partner. The researchers found that women who married or cohabitated during the study gained 9 pounds more than single women, and married or cohabitating men gained, on average, 6 pounds more than single men. (a) Why is this an observational study? What type of observational study is this? (b) What is the response variable in the study? What is the explanatory variable? (c) Identify some potential lurking variables in this study. (d) Can we conclude that getting married or cohabiting causes one to gain weight? Explain.

In Problems 11-22, identify the type of sampling used. A survey regarding download time on a certain website is administered on the Internet by a market research firm to anyone who would like to take it.
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