Inference Statistics

Front

What is a P-value?

Back

A P-value is a conditional probability that measures the strength of evidence against the null hypothesis in a statistical test.

Front

Is the P-value the probability that the null hypothesis is true?

Back

No, the P-value is not the probability that the null hypothesis is true; it is the probability of observing the data, or something more extreme, given that the null hypothesis is true.

Front

What does a small P-value indicate?

Back

A small P-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, leading to its rejection.

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence.

Front

How does sample size affect the width of a confidence interval?

Back

Increasing the sample size generally decreases the width of the confidence interval, providing a more precise estimate of the population parameter.

Front

What is the effect of increasing confidence level on the confidence interval?

Back

Increasing the confidence level (e.g., from 95% to 99%) widens the confidence interval, as it requires a larger range to ensure that the true parameter is captured.

Front

What is a two-sample t-test?

Back

A two-sample t-test is a statistical method used to compare the means of two independent groups to determine if they are significantly different from each other.

Front

When is a two-sample z-test appropriate?

Back

A two-sample z-test is appropriate when comparing the means of two independent groups with known population variances and large sample sizes.

Front

What is the relationship between sample size and the standard error?

Back

The standard error decreases as the sample size increases, leading to narrower confidence intervals.

Front

What does it mean to reject the null hypothesis?

Back

Rejecting the null hypothesis means that the evidence from the sample data is strong enough to conclude that the null hypothesis is unlikely to be true.