As a researcher collects more and more data, the 95% prediction intervals in gen

Question

As a researcher collects more and more data, the 95% prediction intervals in general: A. Become narrower and narrower, but the widths are always more than approximately 4 times the slope. B. Become narrower and narrower, with the widths getting closer and closer to 0. C. Become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate. D. Become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate. As a researcher collects more and more data, the 95% prediction intervals in general: A. Become narrower and narrower, but the widths are always more than approximately 4 times the slope. B. Become narrower and narrower, with the widths getting closer and closer to 0. C. Become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate. D. Become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate. A. Become narrower and narrower, but the widths are always more than approximately 4 times the slope. B. Become narrower and narrower, with the widths getting closer and closer to 0. C. Become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate. D. Become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate.

Explanation / Answer

Since using more and more data means the variance of the sample mean goes closer and closer to 0. Hence the width of the PI (which is directly proportional to the variance if LOC is fixed) goes closer and closer to 0

Hence option B is correct

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