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Chapter 11: Problem 2

Student Center Survey For their class project, a group of Statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. a) Do you think the group was using an SRS? Why? b) What sampling design do you think they used?

Short Answer

Expert verified
a) No, they did not use SRS because of equal representation of each class. b) They likely used stratified sampling.

Step by step solution

01

Understand Simple Random Sampling (SRS)

Simple Random Sampling (SRS) is a sampling technique where each individual from the population has an equal chance of being selected. In the context of this survey, SRS would mean each student, regardless of their year, would have the same probability of being part of the 200 students selected for the survey.
02

Analyze the Sample Distribution

The sample contains precisely an equal number of students from each year: 50 first-year, 50 sophomores, 50 juniors, and 50 seniors. This equal distribution across all class years suggests that not every individual had an equal chance of selection, contradicting the principle of SRS.
03

Evaluate If SRS Was Used

Given the exact number of students from each year, it is unlikely the team used SRS, as this specific distribution would require each of the class years to coincide with a 25% representation purely by chance, which is improbable.
04

Identify the Sampling Design Used

The students likely used a "Stratified Sampling" design. In stratified sampling, the population is divided into distinct subgroups (strata) and samples are drawn from each subgroup. Here, the strata would be the class years: first-year, sophomore, junior, and senior.

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Key Concepts

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

Simple Random Sampling
Simple Random Sampling (SRS) is a foundational concept in statistics that ensures each individual in a population has an equal probability of selection. Imagine you have a big hat filled with names, and you randomly pick out names without looking.

Each name has the same chance of being selected, reflecting the essence of SRS. This method is advantageous because it eliminates biases, making it a favorite among researchers for its simplicity.

However, SRS requires a complete list of the population, which isn't always feasible.
  • Ensures fairness and randomness.
  • Simple to implement with modern tools.
  • Best suited for small populations due to practical limitations.
In the context of the student center survey, the likelihood that each student across all class years (freshmen to seniors) had an equal opportunity to be included doesn't hold, as shown by the equal distribution of sampled students across these years.
Stratified Sampling
Stratified Sampling is a more strategic approach where the population is divided into subgroups, or "strata," and samples are taken from each stratum.

This technique ensures representation from each key segment of the population. For example, the student center survey used strata based on class years鈥攆irst-year, sophomores, juniors, and seniors.

By doing so, it guarantees that insights from each class year contribute equally to the results.
  • Offers greater precision compared to SRS.
  • Effective for heterogeneous populations.
  • Ensures essential segments of the population are not missed.
Stratified sampling can deliver more nuanced insights, especially in diverse populations where segments have varying perspectives.
Statistics Education
Understanding and applying different sampling methods is crucial in statistics education. It not only helps in designing effective surveys but also in interpreting data accurately.

Students learn to discern which sampling technique suits various research contexts, enhancing their analytical skills.

By evaluating the potential biases and efficiencies associated with each method, students gain critical thinking skills necessary for real-world applications.
  • Encourages logical and analytical thinking.
  • Empowers students to critically assess data in studies.
  • Prepares students for advanced statistical challenges.
Courses often involve practical projects, like the student center survey, to bridge theoretical concepts with tangible outcomes, thereby solidifying understanding.
Survey Design
Good survey design is essential for collecting valid and reliable data. When planning surveys, choosing the correct sampling method is paramount.

The survey design must ensure data at every step along the way accurately reflects the population's diverse attributes.

Sampling errors can skew data interpretation and affect the credibility of results.
  • Critical for obtaining actionable insights.
  • Requires defining the research goals clearly.
  • Focuses on minimizing biases and errors.
By paying close attention to survey design principles, one can create a survey that yields meaningful and accurate insights, as the right methods and designs are implemented from the start.

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Most popular questions from this chapter

\- Parent opinion, part 1 In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are some of the ideas proposed for gathering data. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result. a) Put a big ad in the newspaper asking people to log their opinions on the PTA website. b) Randomly select one of the elementary schools and contact every parent by phone. c) Send a survey home with every student, and ask parents to fill it out and return it the next day. d) Randomly select 20 parents from each elementary school. Send them a survey, and follow up with a phone call if they do not return the survey within a week.

\- Accounting Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed properly. a) Propose a sampling strategy for the supervisor. b) How would you modify that strategy if the company makes both wholesale and retail sales, requiring different bookkeeping procedures?

\- Another mistaken poll Prior to the mayoral election discussed in Exercise \(15,\) the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with \(52 \%\) of the vote. The newspaper was wrong: Amabo lost, getting only \(46 \%\) of the vote. Do you think the newspaper's faulty prediction is more likely to be a result of bias or sampling error? Explain.

Texas A \& M Administrators at Texas A\&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A\&M student body has about 46,000 members. a) What problems do you see with asking the following question of students? "Are you the first member of your family to seck higher education?" b) For each scenario, identify the kind of sample used by the university administrators: i. Select several dormitories at random and contact everyone living in the selected dorms. ii. Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. iii. Using a computer-based alphabetical list of registered students, select one of the first 25 on the list by random and then contact the student whose name is 50 names later, and then every 50 names beyond that. c) A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because everyone had an equal opportunity to sit in any seat and because she randomized the choice of rows. What do you think? Be specific. d) For each of these proposed survey designs, identify the problem and the effect it would have on the estimate of the percentage of students who are the first in their family to go to college. i. Publish an advertisement inviting students to visit a website and answer questions. ii. Set up a table in the student union and ask students to stop and answer a survey. e) The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of current A\&M students who are the first in their families to attend college. Explain to the president the difference between the proportion of respondents who are first attenders and the proportion of the entire student body that are first attenders. Use appropriate statistics terminology.

Satisfied workers The managers of a large company wished to know the percentage of employees who feel "extremely satisfied" to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed responses. a) The company's annual report states, "Our survey shows that \(87.34 \%\) of our employees are "very happy" working here." Comment on that claim. Use appropriate statistics terminology. b) One manager suggested surveying employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by \(7 .\) Is this a simple random sample? c) For each scenario suggested by a different manager, determine the sampling method. i. Use the company e-mail directory to contact 150 cmployees from among those employed for less than 5 years, 150 from among those employed for \(5-10\) years, and 150 from among those employed for more than 10 years. ii. Use the company e-mail directory to contact every 50th employce on the list. iii. Select several divisions of the company at random. Within each division, draw an SRS of employees to contact. d) One manager suggested having the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan? e) For each of these designs proposed by a different manager, identify the problem with the method and the effect it would have on the estimate of the percentage of cmployees who feel "extremely satisfied" to work there. i. Leave a stack of surveys out in the employee cafeteria so people can pick them up and return them. ii. Stuff a questionnaire in the mailbox of each employee with the request that they fill it out and return it.
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