If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic? Question 4 options: If the samples are the same size and have the same variance If the samples are the same size and have the same mean If the samples have the same mean and the same variance If the samples are the same size and have the same mean and the same variance

Construct a numerical example, i.e., a data set, such that a two-sample t-test will yield an insignificant test result but a pair t-test will yield a significant test result. (For the two-sample t-test, you can either assume equal variances or unequal variances, which will not affect the key idea of this question.) I need to know how this is possible and what the basics of making this data set should be.

A factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of…

A medical researcher wants to test whether the mean cholesterol levels are the same for 3 treatment groups of subjects (with 18 total randomly selected subjects): those who take a new medication, those who follow a diet, and those who make no changes to medication or diet. They plan to use a 5% level of significance for their decision. Below is a partial Analysis of Variance table. Use it to answer the following questions deg of freedom Sum of Squares Mean Square F statistic Treatment Group 3.121 1.5607 Error 1.517 0.1011 Total 17 What is the critical value of F we would compare this to (see F-table) [ Select ] What is our decision v [ Select ] More information is needed Do not reject the null hypothesis because our f-statistic is smaller than the critical f Reject the null hypothesis because our f-statistic is greater than the critical f Reject the null hypothesis because our f-statistic is smaller than the critical f Do not reject the null hypothesis because our f-statistic is…