Question

Please answer with detail. Thanks in advance!!!

A group of researchers is interested in study the effects of caffeine on memory. They plan to use a sample of 25 adults, with the intention of generalizing the findings to the larger population. One of the researchers is concerned, however, because their sample appears to differ from the population in regards to a characteristic that he believes could hinder the generalization of the caffeine and memory study results.

This characteristic is cortisol level. A confidence interval has been constructed for the average cortisol level of the population: 10 - 15 mcg/dL. The average cortisol level for the sample is 17 mcg/dL.

The concerned researcher argues that because the sample's average cortisol level is not within the confidence interval for the population mean, that the sample is not representative of the population and should not be used for the study. The other researchers in the group argue that the difference doesn't matter, and the fact that the sample is relatively small makes it even less important.

Considering the research topic and purpose, and what confidence intervals represent, do you agree with the concerned researcher? Explain why or why not. Is there anything that the research team could do differently to address this potential problem?

Answer 1

We know that the observed confidence interval range is 10 mcg/dl to 15 mcg/dl and the average cortisol level for the sample is 17 mcg/dl.

it is clear that the average cortisol level for the sample is not inside the confidence interval range, so we can say that it is not a good representatitve of the population because if it is reprensentating the population, then the average must be within the confidence interval range.

sample size used in the study was 25, which is less than 30. We can use t distribtution for smaller sample size, but still the average has to be within the confidence interval range. So, sample size effect is not big in this case on the average sample.

So, we can say that the statement made by concerned researcher is correct.

yes, we can increase the sample size, so that we can have higher chances of average cortisol level within the confidence interval range.