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Roper Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged \(13-65 .\) Their samples are designed so that they get 500 males and 500 females in each country. (www.gfkamerica.com) a) Are they using a simple random sample? Explain. b) What kind of design do you think they are using?

Short Answer

Expert verified
a) No, they are not using a simple random sample. b) They are likely using stratified sampling.

Step by step solution

01

Define Simple Random Sample

A simple random sample is a sampling method where each member of the population has an equal probability of being selected and each sample of size n has an equal chance of being chosen from the given population. This means there is no predetermined structure or subgroup within the sample; each person is selected randomly.
02

Check for Simple Random Sample Usage

The Roper survey chooses 1000 people per country, split evenly between 500 males and 500 females. This indicates that they are not selecting individuals randomly from the entire population. Instead, they have set quotas for gender in each country, meaning the sample composition is pre-determined based on gender.
03

Identify the Sampling Method

The selection method used in the Roper survey addresses predefined quotas (gender division of 500 males and 500 females), which implies they are using a stratified sampling method. In stratified sampling, the population is divided into subgroups (strata) that share similar characteristics. Here, the subgroups are defined by gender within each country.

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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 is a fundamental sampling method in statistics. It refers to a process where every member of the population has an equal chance of being selected. This means no favoritism or bias is involved in picking the samples. The key idea is randomness, ensuring each sample of the same size has the same opportunity of being chosen.

To imagine this, think of a lottery draw where each ticket in the bowl has an equal chance of being pulled out. It's entirely by chance who gets chosen, and there's no consideration given to any specific characteristics or stratification like age, gender, or ethnicity.

Using simple random sampling is beneficial because it prevents any bias in selecting samples, which makes the results more reliable and unbiased. However, it can be challenging to implement if the population is too large or diverse, as it may not fairly represent all segments within the population.
Stratified Sampling
Stratified sampling addresses some of the limitations of simple random sampling. Here, the population is divided into different 'strata' or groups that share similar characteristics, such as age, gender, income level, or any other known criteria.

Once these strata are defined, samples are taken from each subgroup. This ensures that each subgroup is adequately represented in the final sample. Due to this method, comparisons or analyses can be made within subgroups, leading to more precise and insightful data analyses.

Imagine taking surveys within a school. Instead of randomly selecting students from the whole student body, you might choose to sample an equal number of students from each grade level. This reflects stratified sampling, as it ensures every grade level has equitable representation in the survey, leading to more balanced and comprehensive results.
  • Ensures representation from each subgroup
  • Leads to more accurate and relevant data
  • Useful in diverse populations
Consumer Survey
Consumer surveys are one of the critical tools businesses use to understand their customers' preferences, expectations, and behaviors. These surveys collect data directly from consumers to gauge their opinions, satisfaction, and general attitudes toward specific products or services.

Conducting consumer surveys can help businesses in many ways, such as:
  • Identifying market trends and consumer preferences
  • Improving products based on customer feedback
  • Enhancing customer satisfaction and loyalty
The methodology for conducting consumer surveys can vary. Companies can choose either simple random sampling for a general feel or stratified sampling to ensure specific demographics are represented adequately.

The data collected provides invaluable insights and form the backbone of strategic business decisions, tailoring marketing strategies and improving consumer relationships.
Global Research
Global research refers to studies conducted across multiple countries to understand various global issues, attitudes, and behaviors. This type of research involves collecting data from diverse cultural and geographical populations, which can be challenging yet insightful.

Carrying out global research allows organizations to:
  • Understand cultural differences and similarities
  • Evaluate global market opportunities
  • Adapt strategies to different markets
In the context of global research, sampling methods must be chosen carefully. Stratified sampling is often more effective as it allows researchers to ensure proportionate representation from each country or subgroup. For instance, adjusting the sample to include equal numbers of participants by gender in every country can lead to more accurate and meaningful comparisons.

By combining statistical techniques with cultural understanding, global research can provide businesses, policymakers, and academic institutions with actionable insights that consider the complexities of the international landscape.

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Most popular questions from this chapter

\- 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.

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.

\- Roller coasters An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2 -minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10 th person on the line for the roller coaster, starting from a randomly selected individual. a) What kind of sample is this? b) What is the sampling frame? c) Is it likely to be representative?

Cell phone survey What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non-cell phone exchanges. Do you think these advantages and disadvantages have changed over time? How do you expect they'll change in the future?

\- Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little finger will probably have reached the back of your left hand. If the fourth hand width goes past the end of your middle finger, turn your hand sideways and count finger widths to get there. a) How many hand and finger widths is your arm? b) Suppose you repeat your measurement 10 times and average your results. What parameter would this average estimate? What is the population? c) Suppose you now collect arm lengths measured in this way from 9 friends and average these 10 measurements. What is the population now? What parameter would this average estimate? d) Do you think these 10 arm lengths are likely to be representative of the population of arm lengths in your community? In the country? Why or why not?

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