Slovin's Formula: Sample Size Calculation
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Questions and Answers

Using Slovin's formula, if you have a population of 2,500 and desire a 95% confidence level, what is the required sample size?

  • 286
  • 357
  • 333
  • 345 (correct)

A researcher wants to survey a population of 10,000 individuals. They aim for a 98% confidence level. According to Slovin's formula, what should their sample size be, rounded to the nearest whole number?

  • 2041 (correct)
  • 2439
  • 6944
  • 1667

A market research team needs to determine the sample size for a survey with a population of 1,500, using Slovin's Formula. If they are willing to accept a 5% margin of error, what will be the sample size?

  • 300
  • 316 (correct)
  • 214
  • 1429

What is the alpha level (α) associated with a 98% confidence level when using Slovin's formula?

<p>0.02 (B)</p> Signup and view all the answers

A university with 8,000 students wants to survey them about their satisfaction with campus services. If the university uses Slovin's formula with a 95% confidence level, approximately how many students need to be surveyed?

<p>367 (B)</p> Signup and view all the answers

In Slovin's formula, what does 'N' represent?

<p>The total population size. (A)</p> Signup and view all the answers

A small town has a population of 800 residents. The local council wants to conduct a survey to gather opinions on a proposed new park, and they want a 98% confidence level. Using Slovin's formula, what is the minimum sample size they should aim for?

<p>667 (A)</p> Signup and view all the answers

What adjustment should you make to a sample size calculated using Slovin's formula before conducting a survey?

<p>Round to the nearest whole number. (D)</p> Signup and view all the answers

A researcher aims to understand public perception of a new urban development project prior to its implementation. Which data collection method is most suitable for gathering broad opinions efficiently?

<p>Surveys and questionnaires (B)</p> Signup and view all the answers

A clinical psychologist seeks to deeply understand the experiences of a single patient undergoing a novel therapy for PTSD. Which data collection method would provide the most detailed and nuanced insights?

<p>Case studies (A)</p> Signup and view all the answers

An anthropologist wants to study the daily social interactions within a remote tribe without interfering with their natural behavior. Which data collection method is best suited for this type of unobtrusive research?

<p>Observations (A)</p> Signup and view all the answers

To determine if there is a cause-and-effect relationship between sunlight exposure and mood, what research method should be used?

<p>Experiments (D)</p> Signup and view all the answers

A researcher aims to collect detailed accounts of individual experiences during a natural disaster. This requires direct interaction with the affected individuals to gather comprehensive narratives. Which data collection method is most appropriate?

<p>Interviews (C)</p> Signup and view all the answers

A market research firm wants to quickly gauge customer satisfaction with a new product line across a large and diverse customer base. Which data collection method offers the most efficient way to gather this information?

<p>Surveys and questionnaires (C)</p> Signup and view all the answers

A university is performing a study on student success after graduation. They intend to track a group of students over a 10 year period, and analyze what factors contributed to their success. Which research method is most appropriate?

<p>Case Studies (D)</p> Signup and view all the answers

A researcher is hired by the local government to understand why the population in the area is moving away at an alarming rate. The local government wants to take action to solve the problem, and reverse the trend. Which research method should the researcher use?

<p>Surveys and Questionnaires (C)</p> Signup and view all the answers

In a study examining the effects of a new teaching method on student test scores, which of the following would be considered the population?

<p>All students in the school or district where the new method is being tested. (C)</p> Signup and view all the answers

A researcher wants to study the political opinions of college students in the United States. Due to resource constraints, they only survey students at 50 randomly selected universities. What does the group of students at those 50 universities represent?

<p>A sample. (D)</p> Signup and view all the answers

Which of the following is the best example of a qualitative variable?

<p>The primary language spoken at home. (C)</p> Signup and view all the answers

A researcher is studying consumer preferences for different brands of coffee. Which type of data is being collected if the researcher asks participants to rank the coffee brands from most to least preferred?

<p>Qualitative. (C)</p> Signup and view all the answers

Which scenario involves collecting quantitative data?

<p>Measuring the reaction time of participants in a cognitive task. (D)</p> Signup and view all the answers

A professor records the final grades (A, B, C, D, or F) of students in a class. Is this data qualitative or quantitative?

<p>Qualitative, because grades represent categories of performance rather than numerical measurements. (A)</p> Signup and view all the answers

A study aims to determine if there is a correlation between the number of hours students study per week and their GPA. What type of variables are 'hours of study' and 'GPA' in this study?

<p>Both are quantitative variables. (C)</p> Signup and view all the answers

Which of the following best illustrates the use of both qualitative and quantitative variables in a single study?

<p>Interviewing customers about their satisfaction levels (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied) and recording their ages. (A)</p> Signup and view all the answers

A researcher is planning a study in a city with a population of 1,500 people. Using Slovin's formula, what is the minimum sample size required if the researcher wants a 4% margin of error?

<p>306 (C)</p> Signup and view all the answers

In a town with a population of 2,000 people, a survey is conducted with a sample size of 400. What is the margin of error used for this survey based on Slovin's Formula?

<p>0.033 (B)</p> Signup and view all the answers

A data set is collected to analyze customer satisfaction. Which of the following statements best describes the relationship between the data points and the data set?

<p>Each data point is a piece of information gathered, and collectively, they form the data set. (C)</p> Signup and view all the answers

In the context of data collection, how are samples and populations related to the concept of sets?

<p>A sample is a finite set of observations representing a subset of the entire population, and the population can be considered an infinite set. (A)</p> Signup and view all the answers

A company is trying to determine the effectiveness of a new marketing strategy. What is the role of statistics in this scenario?

<p>Statistics are used to collect, organize, and interpret data to understand market trends and devise solutions. (D)</p> Signup and view all the answers

A researcher is studying the heights of all students at a university. In this context, what does the 'population' refer to?

<p>The set of all students currently enrolled at the university. (D)</p> Signup and view all the answers

A market research company decides to survey a sample of households in a city to estimate the average household income. If the city has a total of 10,000 households, and the company uses Slovin's formula with a 5% margin of error to determine the sample size, approximately how many households should they survey?

<p>385 (C)</p> Signup and view all the answers

A quality control engineer wants to estimate the proportion of defective items produced in a factory. They plan to sample from the production line. Which statement accurately describes the relationship between the sample and the population in this context?

<p>The sample is a subset of all items produced, and the population consists of all items produced. (C)</p> Signup and view all the answers

When is Slovin's formula most appropriate for determining sample size?

<p>When there is minimal or no prior knowledge about the population's characteristics. (A)</p> Signup and view all the answers

A researcher aims for a 95% confidence level in their study. According to the information provided, what would be the corresponding error tolerance (e) to use in Slovin’s formula?

<p>0.05 (C)</p> Signup and view all the answers

Given a population of 500, which calculation correctly applies Slovin's formula to determine the sample size needed with an error tolerance of 0.05?

<p>$n = \frac{500}{1 + 500 \times 0.05^2}$ (A)</p> Signup and view all the answers

A town has a total population of 2,000 residents. If a researcher uses Slovin's formula with an error tolerance of 0.03 to determine the sample size for a survey, approximately how many residents should be surveyed?

<p>667 (D)</p> Signup and view all the answers

What happens to the required sample size calculated by Slovin's formula as the error tolerance (e) increases, assuming the population size stays constant?

<p>The sample size decreases. (B)</p> Signup and view all the answers

A market research firm is planning to survey a city with a population of 50,000. They decide to use Slovin's formula because they lack detailed information about residents' preferences. Which error tolerance would result in the smallest sample size?

<p>0.10 (D)</p> Signup and view all the answers

When using Slovin's formula, if a researcher decreases the error tolerance from 0.05 to 0.01, how is the necessary sample size affected?

<p>The sample size will increase significantly. (B)</p> Signup and view all the answers

Flashcards

Slovin's Formula

A formula used to calculate the minimum sample size needed for a study.

Data Collection

The process of gathering information for analysis.

Data Set

A collection of related data points.

Sample

A limited selection from a larger group.

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Population

A complete group to get data from.

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Subset

A representative part of a group.

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Statistics

Deals with collecting, organizing, and interpreting data.

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Population (in statistics)

All possible cases from which data are collected.

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Variables

Characteristics that can change or vary.

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Qualitative Variable

Focuses on qualities or characteristics.

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Quantitative Variable

Measures a numerical quantity.

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Qualitative (Example)

Identifying the color of each car.

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Quantitative (Example)

Determining the number of students.

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Qualitative Data (Example.)

Rating a movie as 'excellent', 'good', or 'poor'.

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Sampling in Statistics

Looking at a population's behavior by examining a subset.

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Error Tolerance (e)

How much error you're willing to accept in your sample results.

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Calculating Error Tolerance

Subtract your confidence level from 1 (1 - confidence level).

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Slovin's Formula Equation

n = N / (1 + N(e^2)) where n=sample size, N=population size, e=error tolerance.

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Population Size (N)

The size of the total group you're studying.

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Sample Size (n)

The number of individuals you need to survey.

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What is the margin of error?

The acceptable range of error in your sample results.

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What is confidence level?

The level of certainty that the true population value falls within your margin of error.

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What is alpha level (e)?

Represents the probability of making a wrong conclusion about the population

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What is Slovin's Formula?

Use this formula to calculate the sample size needed for a survey

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What is population size (N)?

The total number of individuals in your group of interest.

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What is Sample size (n)?

The number of individuals you need to survey or study.

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Rounding the sample size

Round the result of Slovin's formula to the next whole number

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If N=1000 and e=0.05, what is n?

n = 1000 / (1 + 1000 * 0.05^2) = 286

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Surveys

Asking predetermined questions to gather information about opinions, behaviors, or characteristics.

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Interviews

Direct interaction between a researcher and a participant to ask questions and record responses.

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Observations

Directly watching and recording behavior or events without interacting with participants.

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Experiments

Manipulating variables to observe the effect on the outcome, under controlled conditions, to establish cause-and-effect.

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Case Studies

In-depth investigation of a single case or small number of cases to gain insights into complex phenomena.

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Questionnaires

Gathering information through asking a set of questions.

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In-depth Investigations

Used for qualitative research, exploring complex issues in detail.

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Public Opinion Polls

Gathering information about opinions, behaviors, or characteristics from a large group.

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Study Notes

  • Statistics looks at a population's behavior by taking a sample.
  • It can be impossible to survey an entire population due to money or time constraints.
  • Surveying samples are preferrable among researchers to surveying an entire population.
  • Slovin's formula is used when there is no pre-existing information about a population.
  • Slovin formulated the Slovin's formula in 1960.
  • Use the formula to figure out what sample size to take.

Slovin's Formula

  • Formula: n = N / (1 + Ne^2),
  • n = Number of samples
  • N = Total population
  • e = Error tolerance level

Example question

  • Use question to find out what sample of population of 1,000 people, taking a survey on soda preferences:

  • Step 1: Figure out your confidence level:

  • e = 1.00 - 0.95 = 0.05

  • e = 1.00 - 0.98 = 0.02.

  • You might want a confidence level of 95% (alpha level of 0.05), good accuracy at the 98% confidence level (alpha level of 0.02).

  • Step 2: Use your data in the formula

  • Use a 95% confidence level

  • Population size of 1,000

  • N = 1000

  • e = 0.05

  • n = 285.7142857

  • Step 3: Round your result:

  • 285.7142857 = 286

Data set

  • Each piece of gathered information is a data point that makes up a data set.
  • A sample represents a set of finite observations.
  • Population can be considered an infinite set.
  • Collected data in sampling represents a subset of a population.

Definitions

  • Statistics: Branch collecting, organizing, and interpreting data to address real world topics.
  • Population: Set of all possible cases from which data is collected.
  • Ex: A study regarding the average height of students requires the population of all the students in the school.
  • Sample:A subset.
  • Variables: Vary over time from subject to subject.
  • Qualitative variable: Focuses on quality/characteristics of an experimental unit.
  • Ex: civil status/gender/color
  • Quantitative variable: Measures numerical quantity of experimental unit.
  • Ex: age, height, weight, daily allowance

Data Collection Methods

  • Surveys and Questionnaires: Predetermined questions gathering opinions/behaviors.
  • This is used in social sciences, market research, and public opinion polls, is cost effective, standardised format.
  • Disadvantage is the response bias and a limited depth of information
  • Interviews: Direct interaction, questions asked and recorded.
  • Useful in qualitative research, case studies, and in-depth investigations that allows in-depth exploration, flexibility in questions.
  • Disadvantage is its time consuming, potential for interviewer bias
  • Observations: Observe and record behavior, events, or phenomena without interaction.
    • Used in realism research, which gives firsthand information, minimizes response bias.
    • Disadvantage is the observer bias and limited insight into underlying motivations
  • Experiments: Manipulate variables to observe the effect on the outcome.
  • Helpful in natural science due to controlled conditions help provide case and effect relationships.
  • Disadvantage is artificial settings and ethical concerns may limit generalizability.
  • Case Studies: Examination of a single person or small people for insight.
  • Useful in psychology, medicine, and social science since it is suitable for complex/unique cases.
  • Disadvantage is limited data with potential research bias.

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Description

Learn about Slovin's formula, used to determine sample size when population information is limited. This formula helps researchers efficiently survey a representative sample, balancing accuracy and resources. Understand how to apply Slovin's formula with practical examples.

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