Which of the following statements about a 95% confidence interval is true? Select 2 correct answers.

A. There is a 95% chance the population mean lies within the interval.
B. If we were to take many samples, approximately 95% of the calculated intervals would contain the population mean.
C. The sample mean will always fall within the confidence interval.
D. The interval width can change based on sample size and confidence level.

The correct statements about a 95% confidence interval are B and D. Statement B indicates that approximately 95% of intervals from repeated samples will contain the population mean, while statement D explains that the interval width can vary with sample size and confidence level.
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Answered by Anonymous | 2025-07-04

When discussing confidence intervals, particularly the 95% confidence interval, it's crucial to understand what these intervals represent in statistical terms.

Statement (A) : 'There is a 95% chance the population mean lies within the interval.'
This statement is not true. A 95% confidence interval means that if we were to take many different samples and compute confidence intervals for each sample, then about 95% of these intervals would contain the actual population mean. It doesn't state there is a 95% chance that the specific interval calculated from a single sample contains the population mean.

Statement (B) : 'If we were to take many samples, approximately 95% of the calculated intervals would contain the population mean.'
This statement is true. This is a fundamental definition of the 95% confidence interval. It reflects the process of taking numerous samples and forming intervals using each one; roughly 95% of those intervals should encompass the true population mean.

Statement (C) : 'The sample mean will always fall within the confidence interval.'
This statement is not necessarily true. While the confidence interval is computed using the sample mean, the interval could extend in such a way that it doesn't fully encompass the sample mean, especially if the data distribution is skewed or if there are outliers.

Statement (D) : 'The interval width can change based on sample size and confidence level.'
This statement is true. The width of a confidence interval is influenced by the sample size - larger sample sizes typically result in narrower intervals - and the confidence level - higher confidence levels result in wider intervals, assuming other factors remain constant.


Thus, the correct statements are (B) and (D) .

Answered by danjohnbrain | 2025-07-06