Understanding Confidence Intervals

Why are confidence intervals important in statistics?

• They provide an exact value of the population parameter.

• They allow estimation of population parameters using samples.

• They eliminate the need for sampling.

• They guarantee the true parameter value.

What is a common misconception about the 95% confidence interval?

• It is the same as a credible interval.

• It indicates a 95% chance the true parameter is within the interval.

• It is only applicable to large samples.

• It provides a range for the sample mean.

In frequentist statistics, how is the true parameter treated?

• As a fixed but unknown quantity.

• As a random variable with a distribution.

• As a known and fixed value.

• As a variable that changes with each sample.

What does the correct interpretation of a 95% confidence interval imply?

• The true parameter is always within the interval.

• The interval is only valid for one sample.

• 95% of the time, the interval will contain the true parameter.

• The interval is always accurate.

How does the Bayesian approach differ from the frequentist approach?

• It treats parameters as fixed values.

• It uses prior distributions to reflect uncertainty.

• It does not use probability distributions.

• It is not concerned with sample data.

What is a credible interval in Bayesian statistics?

• An interval that does not require prior knowledge.

• An interval that is always wider than a confidence interval.

• An interval that reflects the probability of a parameter within a range.

• An interval that contains the true parameter with 100% certainty.

What is the main criticism of Bayesian statistics?

• It may be influenced by subjective inputs.

• It cannot incorporate prior knowledge.

• It does not use prior distributions.

• It is too objective.

How is the confidence interval for the mean calculated if data is normally distributed?

• Using the population mean and standard deviation.

• Using the sample mean, standard deviation, and sample size.

• Using the sample mean and variance only.

• Using the sample size and variance only.

What is the z-value for a 95% confidence level?

• 2.33

• 2.58

• 1.96

• 1.64

What does the 95% confidence level refer to?

• The certainty of the true parameter value.

• The accuracy of the sample data.

• The long-run reliability of the method used.

• The probability of the sample mean being correct.