Homework Often one wants to compare two treatments or populations and determine if there is a difference. This can be done either with or without matching. The various assumptions made in this situation primarily affects the appropriate number of degrees of freedom to be used. This can range from one less than the smallest sample to two less than the sum of the sample sizes with various values inbetween possible.

Testing the significance of the slope of the regression line In this section we test the value of the slope of the regression line. Figure 1 shows the worksheet for testing the null hypothesis that the slope of the regression line is 0.

We can also test whether the slopes of the regression lines arising from two independent populations are significantly different.

This would be useful for example when testing whether the slope of the regression line for the population of men in Example 1 is significantly different from that of women. I have added the appropriate labels manually for clarity.

A18,TRUE,TRUE for data in Figure 1 R Square is the correlation of determination r2 see Definition 2 of Basic Concepts of Correlationwhile all the other values are as described above with the exception of the standard error of the y-intercept, which will be explained shortly.

Excel also provides a Regression data analysis tool. The creation of a regression line and hypothesis testing of the type described in this section can be carried out using this tool. Figure 3 displays the principal output of this tool for the data in Example 1. Figure 3 — Output from Regression data analysis tool The following is a description of the fields in this report: Multiple R — correlation coefficient see Definition 1 of Multiple Correlationalthough since there is only one independent variable this is equivalent to Definition 2 of Basic Concepts of Correlation R Square — coefficient of determination see Definition 1 of Multiple Correlationi.

The third table gives key statistics for testing the y-intercept Intercept in the table and slope Cig in the table. We will explain the intercept statistics in Confidence and Prediction Intervals for Forecasted Values. The slope statistics are as follows: Figure 4 — Additional output from Regression data analysis tool for data Residual Output: There is also the option to produce certain charts, which we will review when discussing Example 2 of Multiple Regression Analysis.Q: Indicate which assumptions are needed to use the sample mean and normal tables to test a hypothesis about a population mean, MU, and known variance, SIGMA**2.

Alan, If the p-value for the one-tail test is say, then for a symmetric distribution the p-value for the two-tailed test is, which you can compare with alpha (say). •Prefer to believe truth does not lie with null hypothesis. We conclude that there is a statistically significant difference between average fat loss for the two methods.

What is hypothesis testing?(cont.) The hypothesis we want to test is if H 1 is \likely" true. So, there are two possible outcomes: Reject H 0 and accept 1 because of su cient evidence in the sample in favor or H.

it follows that ρ = 0 if and only if β = 0. Thus Theorem 1 of One Sample Hypothesis Testing for Correlation can be transformed into the following test of the hypothesis H 0: β = 0 (i.e.

the slope of the population regression line is zero): Example 1: Test whether the slope of the regression line. The question of whether one should run A/B tests (a.k.a online controlled experiments) using one-tailed versus two-tailed tests of significance was something I didn’t even consider important, as I thought the answer (one-tailed) was so self-evident that no discussion was necessary.

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