Question 36

Increasing the sample size decreases the width of the confidence interval.

By increasing the sample size, the researcher can decrease the width of the confidence interval, leading to a more precise estimate of the population parameter.

A) Increase the sample size

This option is correct because a larger sample size reduces the standard error, which in turn decreases the width of the confidence interval. A smaller width indicates a more precise estimate, allowing the researcher to make stronger inferences about the population.

B) Increase the level of confidence

This option is incorrect as increasing the level of confidence actually widens the confidence interval. A higher confidence level means that the researcher wants to be more certain that the interval contains the true parameter, which necessitates a broader range.

C) Collect another sample

This option is not necessarily effective. While collecting another sample could provide different data, it does not guarantee a decrease in the width of the confidence interval unless the new sample size is larger than the original. Without specifying that the sample size is increased, this action alone cannot ensure a reduction in width.

D) Use a different estimator

This option is also incorrect. Using a different estimator may change the point estimate but does not inherently change the width of the confidence interval. The width is primarily determined by the sample size and the variability of the data, not by the choice of estimator.

Conclusion

Increasing the sample size is the definitive method for decreasing the width of the confidence interval, enhancing the precision of the estimate. All other options either increase the width or do not guarantee a reduction, failing to address the core concept of statistical estimation effectively.