Question

In a series of journal articles, investigator A reported her data, which are approximately normally distributed, in terms of a mean plus or minus two standard deviations, while investigator B reported his data in terms of a mean plus or minus two standard errors of the mean. The difference between the two methods is

		investigator A is estimating the extreme percentiles, whereas investigator B is estimating the most usual percentiles
		investigator A is estimating the range that she thinks contains 95% of the means, whereas investigator B is estimating the range that he thinks contains 95% of the medians
		investigator A is estimating the range that she thinks contains about 95% of her data values, whereas investigator B is estimating the range that he thinks (with 95% confidence) contains the true mean being estimated
		investigators A and B are really estimating the same range, but are just using different systems of reporting
		none of the above

Answer 1

Ans :

investigator A is estimating the range that she thinks contains about 95% of her data values, whereas investigator B is estimating the range that he thinks (with 95% confidence) contains the true mean being estimated

Explanation for investigator A part of the question

investigator A reported her data, which are approximately normally distributed, in terms of a mean plus or minus two standard deviations

by 68-95-99 rule of normal distribution

68% of the data is within 1 standard deviation of the mean ,  95% of the data is within 2 standard deviations of the mean and 99.7% of the data is within 3 standard deviations of the mean.

so therefore, Investigator A thinks 95% of the data is within 2 standard deviations of the mean i.e

investigator A is estimating the range that she thinks contains about 95% of her data values,

investigator B reported his data in terms of a mean plus or minus two standard errors of the mean

95% Confidence interval formula

sample mean Z_0.025 Standard error.

Z_0.025 = 1.96 2

Therefore, mean plus or minus two standard errors of the mean represents the 95% confidence interval estimate for the true mean.

i.e

investigator B is estimating the range that he thinks (with 95% confidence) contains the true mean being estimated