25 Questions
What is the relationship between sample size and sampling error?
As sample size increases, sampling error decreases.
If a survey has a margin of error of 4.2 percentage points, what does this imply about the population proportions?
The population proportions could differ by ±4.2% from the sample proportions.
How does the level of confidence affect the margin of error?
Higher confidence levels result in larger margins of error.
What impact does a small sample size have on sampling error?
Small sample sizes lead to larger sampling errors.
Why do managerial issues influence sample size in probability samples?
To ensure that the sample accurately represents the population.
How does the number of subgroups analyzed affect sampling error?
Analyzing more subgroups increases sampling error.
What is the purpose of determining the sample size based on budget available?
To control costs while maximizing data quality.
Why is it crucial to consider confidence level when determining the margin of error?
'Confidence level' determines how certain you are that the true value falls within the margin of error.
What does a 90% confidence level imply about the range of results obtained?
It means you can be 90% confident that your results fall within a specific range.
What is a key consideration when determining whether a sample size is adequate?
Whether the margin of error meets client expectations.
What is the relationship between sample size and sampling error?
As sample size increases, sampling error decreases.
How does the level of confidence affect the margin of error?
Higher confidence levels result in larger margins of error.
Why do managerial issues influence sample size in probability samples?
To guarantee the true population values are included in the chosen confidence interval.
What impact does a small sample size have on sampling error?
It increases sampling error.
How does the number of subgroups analyzed affect the accuracy of results?
Analyzing more subgroups decreases the accuracy.
What does a 90% confidence level imply about the margin of error?
The margin of error is wider than at 95% confidence.
Why is it crucial to consider budget availability when determining sample size?
To make practical decisions about the sample size based on funding restrictions.
What is the purpose of determining sample size based on past experience or client input?
To tailor the study to meet specific needs
How do financial considerations play a role in determining sample size?
They may constrain the maximum sample size feasible
What is significant about having a 95% confidence level when calculating margins of error?
It indicates a high degree of certainty about the findings
What is the relationship between sample size and sampling error?
As sample size increases, sampling error decreases.
Why is it essential to consider the confidence level when calculating margins of error?
Confidence level affects the precision of the margins of error.
How does budget availability typically influence sample size determination?
Budget availability often partially determines the sample size.
Why does the number of subgroups analyzed pose a challenge in interpreting the results?
Increased subgroups make it harder to distinguish real differences from sampling error.
What impact does a small sample size have on the margin of error?
A small sample size widens the margin of error.
Study Notes
Determining Sample Size for Probability Samples
- The process involves financial, managerial, and statistical issues.
- Larger samples lead to smaller sampling errors and margins of error.
- Margin of error is a confidence interval around the sample statistic within which the population parameter is expected to be.
- It measures how many percentage points the results differ from the real population value.
Managerial Issues
- Managerial issues influence sample size based on confidence in including true population values in the chosen confidence interval.
- A survey with a 3.1 percentage point margin of error means the population proportions are expected to be within +/- 3.1 percentage points from the sample proportions.
- Managers must consider whether a 6.2 percent range is acceptable.
Budget Availability
- Budget availability sometimes determines sample size, which is not a scientific approach.
- Clients may specify the sample size they want (e.g., 100, 200, 300, 400, 500, etc.) based on past experience or personal judgment.
- Researchers must determine whether the requested sample size is adequate and inform the client.
Number of Subgroups Analyzed
- Sample size affects the accuracy of subgroup analysis.
- As sample size gets smaller, sampling error increases, making it harder to determine whether differences between groups are real or due to sampling error.
Confidence Level
- Confidence level is the probability that a particular interval includes the true population value.
- Margin of error is usually produced for one of four confidence levels: 99%, 95%, 90%, or 85%.
- A 95% confidence level means the true percentage for the population will be within the margin of error 95% of the time.
Margin of Error Example
- A survey found 45% of respondents would vote for Candidate A and 42% for Candidate B with a 3% margin of error and 95% confidence level.
- This means we can be 95% confident that support for Candidate A in the population is 45% +/- 3% (42% - 48%).
Learn about the process of determining sample size for probability samples, including financial, managerial, and statistical considerations. Understand the relationship between sample size, sampling error, and margin of error in statistical analysis.
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