Statistical Concepts and Inference Flashcards

A 95% confidence interval for a population mean means which of the following?

Answer: If we repeated sampling many times, about 95% of such intervals would contain the true mean

A confidence level refers to the long-run proportion of constructed intervals that capture the true parameter, not the probability for a single fixed interval.

Which of the following increases the width of a confidence interval, all else equal?

Answer: Increasing the population variance

Greater population variance increases the standard error, widening the interval.

A Type I error in hypothesis testing is best described as:

Answer: Rejecting a true null hypothesis

A Type I error is a false positive: rejecting a null hypothesis that is actually true.

What does the p-value represent?

Answer: The probability of observing data at least as extreme as the sample, assuming the null is true

A p-value is the probability of results as or more extreme than observed under the assumption the null hypothesis holds.

The Central Limit Theorem states that, for a large sample size, the sampling distribution of the sample mean is approximately:

Answer: Normal regardless of population distribution

The CLT guarantees the sample mean's distribution approaches normality as sample size grows, no matter the population shape.

Statistical power is the probability of:

Answer: Rejecting the null when the alternative is actually true

Power is the probability of correctly rejecting a false null hypothesis, equal to 1 minus the Type II error rate.

Which factor does NOT increase statistical power?

Answer: Smaller significance level (alpha)

Decreasing alpha makes it harder to reject the null, which reduces power.