All Flashcards
Explain the importance of random sampling.
Random sampling ensures that the sample is representative of the population, reducing bias and allowing for valid inferences.
Explain the importance of random assignment in experiments.
Random assignment ensures that any observed differences between treatment groups are due to the treatment itself, rather than confounding variables.
Explain the meaning of a 95% confidence level.
If we were to take many samples and construct 95% confidence intervals, about 95% of those intervals would contain the true difference in population means.
How does sample size affect the width of a confidence interval?
Increasing the sample size decreases the width of the confidence interval, providing a more precise estimate of the population parameter.
What does it mean if a confidence interval for the difference of two means contains zero?
It suggests that there is no significant difference between the means of the two populations, as zero is a plausible value for the difference.
What is a point estimate?
The best guess for the true difference in population means, calculated as .
What is the margin of error?
The amount added and subtracted from the point estimate to create the confidence interval.
What is the Central Limit Theorem (CLT)?
If sample sizes are at least 30 (n ≥ 30), the sampling distributions will be approximately normal.
What is the 10% condition?
When sampling without replacement, the sample size should be less than 10% of the population size.
Define critical t-value ().
The value from the t-distribution used in calculating the margin of error, based on the confidence level and degrees of freedom.
What are the differences between random sampling and random assignment?
Random Sampling: Selecting individuals randomly from a population to be in the sample. | Random Assignment: Assigning participants to different treatment groups randomly in an experiment.
What are the differences between the t-distribution and the normal distribution?
T-distribution: Used when the population standard deviation is unknown and estimated by the sample standard deviation, heavier tails. | Normal Distribution: Used when the population standard deviation is known or with large sample sizes due to CLT, lighter tails.
What are the differences between Type I and Type II error?
Type I error: Rejecting the null hypothesis when it is true (false positive). | Type II error: Failing to reject the null hypothesis when it is false (false negative).
What are the differences between standard deviation and standard error?
Standard deviation: Measures the spread of data in a single sample. | Standard error: Measures the variability of the sample statistic (e.g., sample mean) across multiple samples.
What are the differences between confidence intervals and hypothesis tests?
Confidence Intervals: Estimate a population parameter with a range of plausible values. | Hypothesis Tests: Assess the evidence against a specific claim about a population parameter.