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 are the degrees of freedom for the treatment groups? What are the degrees of freedom for the error? What is the F-statistic for this data (3 decimal places)

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.

please don't provide hand writtin solution....

The variance in a production process is an importance measure of the quality of the process. A large variance often signals an opprotunity for improvement in the process by finding ways to reduce the process variance. The conduct a statistical test to determine whether there is a significant differeence between the variance in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?    Machine 1 Machine 2 2.95 3.22 3.45 3.30 3.50 3.34 3.75 3.28 3.48 3.29 3.26 3.25 3.33 3.30 3.20 3.27 3.16 3.38 3.20 3.34 3.22 3.35 3.38 3.19 3.90 3.35 3.36 3.05 3.25 3.36 3.28 3.28 3.20 3.30 3.22 3.28 2.98 3.30 3.45 3.20 3.70 3.16 3.34 3.33 3.18   3.35   3.12   Please use excel