All Flashcards
Explain the concept of confidence level in the context of confidence intervals.
The percentage of times that the confidence interval will contain the true population parameter if the study is repeated many times.
Explain the importance of checking conditions before constructing a confidence interval.
Ensures the t-interval is valid and the results are reliable. Violating conditions can lead to inaccurate conclusions.
Explain how sample size affects the width of a confidence interval.
Larger sample sizes generally lead to narrower (more precise) confidence intervals.
Explain how the standard deviation of residuals affects the width of a confidence interval.
A larger standard deviation of residuals leads to a wider (less precise) confidence interval.
Explain the relationship between confidence level and the width of a confidence interval.
Higher confidence levels lead to wider confidence intervals because you need a larger range to be more confident you've captured the true population parameter.
What are the differences between the t-distribution and the normal distribution?
T-distribution: Used when population standard deviation is unknown, heavier tails | Normal distribution: Used when population standard deviation is known, lighter tails.
What are the differences between a point estimate and a confidence interval?
Point estimate: Single value estimate of a parameter | Confidence interval: Range of plausible values for a parameter.
What are the differences between the standard deviation and the standard error of the slope?
Standard deviation: Measures the spread of data around the mean | Standard error of the slope: Measures the variability of the sample slope.
What are the differences between a 90% confidence interval and a 99% confidence interval?
90% CI: Narrower, less confidence | 99% CI: Wider, more confidence.
What are the differences between interpreting a confidence interval and interpreting a confidence level?
Confidence Interval: Provides a range for the true parameter. | Confidence Level: Indicates the success rate of the method if repeated many times.
Define confidence interval.
A range of values likely to contain the true population parameter.
What is a point estimate?
The single best estimate of a population parameter, like the sample slope.
Define margin of error.
The 'buffer zone' around the point estimate, calculated using the t-score and standard error.
What are residuals?
The differences between observed y-values and y-values predicted by the regression line.
Define standard deviation of residuals.
Measures the spread of data points around the regression line; also known as the standard error of the estimate.