A researcher wants to collect data to create a confidence interval. Which change can the researcher make to increase the level of confidence?

Rationale

Increase the sample size.

Increasing the sample size enhances the level of confidence in a confidence interval by reducing the margin of error and producing more reliable estimates of the population parameter. A larger sample provides better representation of the population, leading to a narrower interval that can confidently estimate where the true parameter lies.

A (Use a different estimator) YOUR ANSWER

Changing the estimator does not inherently affect the level of confidence in the resulting confidence interval. While some estimators may be more efficient or unbiased, the choice of estimator alone does not impact the size of the confidence interval or the confidence level if the sample size remains constant.

B (Collect another sample) YOUR ANSWER

Collecting another sample can provide additional data but does not guarantee an increase in the level of confidence. If the new sample's size remains the same as the original, the confidence level will not improve. The key to increasing confidence lies in the overall sample size rather than simply adding one more sample.

C (Decrease the sample size) YOUR ANSWER

Decreasing the sample size would actually lead to a wider confidence interval and a lower level of confidence. A smaller sample size increases variability and uncertainty in the estimates, thereby negatively impacting the reliability of the confidence interval.

D (Increase the sample size) CORRECT

Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This improvement in precision allows for a higher level of confidence in estimating the population parameter, as the estimates become more stable with larger data sets.

Conclusion

To enhance the level of confidence in a confidence interval, the most effective method is to increase the sample size. This approach minimizes the margin of error and leads to more precise estimates, ensuring that the interval more accurately captures the true population parameter. Other options, like changing estimators or decreasing sample size, do not contribute positively to achieving a higher confidence level.

A researcher wants to collect data to create a confidence interval. Which change can the researcher make to increase the level of confidence?

Increase the sample size.

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