How confidence intervals are constructed and interpreted for means and proportions. Front: the term or scenario. Back: a plain-language explanation.
27 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a confidence interval?
- A range of values computed from sample data that is likely to contain the true population parameter with a specified level of confidence.
- What does a 95% confidence level mean?
- If we repeated the sampling process many times and computed a confidence interval each time, approximately 95% of those intervals would contain the true population parameter.
- What is the margin of error?
- The distance from the point estimate to the boundary of the confidence interval; it represents the maximum expected difference between the sample estimate and the true population value.
- What is standard error?
- The standard deviation of the sampling distribution of a statistic; it measures how much sample statistics vary from one sample to another.
- When do you use z-scores versus t-scores for a confidence interval for a mean?
- Use z-scores when the population standard deviation is known or when the sample is large (typically n > 30). Use t-scores when the population standard deviation is unknown and the sample is small.
- What is the general formula structure for a confidence interval for a mean?
- Sample mean plus or minus (critical value times standard error of the mean).
- What conditions must be met for constructing a valid confidence interval for a mean?
- The data must be a random sample, and either the population must be normally distributed or the sample must be large enough (n > 30) for the Central Limit Theorem to apply.
- How does increasing the sample size affect the width of a confidence interval?
- It decreases the width. A larger sample produces a smaller standard error, which shrinks the margin of error.
- How does increasing the confidence level affect the width of a confidence interval?
- It increases the width. A higher confidence level requires a larger critical value, which widens the margin of error.
- What is a critical value in a confidence interval?
- The value from the z or t distribution that marks the boundary of the central region containing the specified confidence level, such as 1.96 for 95% confidence with z.
- What is the formula for the standard error of the sample mean?
- Standard error equals the population standard deviation divided by the square root of the sample size, or sigma divided by sqrt(n). When sigma is unknown, use the sample standard deviation.
- In what realistic situation is the population standard deviation known?
- It is rarely known in practice. When assumed known, it is usually based on historical data or prior studies, not actual knowledge of the population.
- What distribution is used when the population standard deviation is unknown?
- The t-distribution. It has heavier tails than the normal distribution and accounts for the extra uncertainty from estimating the standard deviation from the sample.
- What is a confidence interval for a proportion?
- A range of values computed from sample proportion data that is likely to contain the true population proportion, constructed as sample proportion plus or minus (critical value times standard error of the proportion).
- What conditions must be met for a valid confidence interval for a proportion?
- The data must be a random sample, and both n times p-hat and n times (1 minus p-hat) must be at least 10 to 15, ensuring both successes and failures are adequately represented.