Question 37

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

A researcher can decrease the width of a confidence interval by increasing the sample size, which provides more information about the population and leads to a more precise estimate.

A) Increase the sample size

This option is correct because a larger sample size results in a smaller standard error, which directly affects the width of the confidence interval. With more data points, the estimate of the population parameter is more reliable, thereby narrowing the interval.

B) Increase the level of confidence

This option is incorrect. Increasing the level of confidence actually widens the confidence interval. A higher confidence level means the researcher is willing to accept a broader range to ensure that the true parameter lies within that interval.

C) Decrease the sample size

This option is incorrect. Decreasing the sample size would increase the standard error, resulting in a wider confidence interval. Fewer data points lead to less certainty about the population parameter.

D) Use a different estimator

This option is not necessarily correct or incorrect without additional context. While some estimators may yield narrower confidence intervals, the effect depends on the estimator's properties and the specific situation. It does not guarantee a decrease in interval width like increasing the sample size does.

Conclusion

Increasing the sample size is the most effective method for decreasing the width of a confidence interval, as it enhances the precision of the estimate. Other options either fail to achieve this goal or lead to the opposite effect, highlighting the importance of sample size in statistical inference.