## One can never prove the truth of a statistical (null) hypothesis.

### Lesson 12: Hypothesis Testing for a Population Mean

We now use the five-step procedure to test the research hypothesis that the mean weight in men in 2006 is more than 191 pounds. We will assume the sample data are as follows: n=100, =197.1 and s=25.6.

### Hypothesis Testing of a Single Population Mean

A major issue for the methodology is the selection of input data, and one possibility for generating the MVO inputs is to use historical data. The simplest way to convert N years of historical data into MVO inputs is to make the hypothesis that the upcoming period will resemble one of the N previous periods, with a probability 1/N assigned to each.

The prevalence of CVD (or proportion of participants with prevalent CVD) among non-smokers is 298/3,055 = 0.0975 and the prevalence of CVD among current smokers is 81/744 = 0.1089. Here smoking status defines the comparison groups and we will call the current smokers group 1 (exposed) and the non-smokers (unexposed) group 2. The test of hypothesis is conducted below using the five step approach.

## Analysis of Variance 3 -Hypothesis Test with F-Statistic

Here we illustrate the use of a matched design to test the efficacy of a new drug to lower total cholesterol. We also considered a parallel design (randomized clinical trial) and a study using a historical comparator. It is extremely important to design studies that are best suited to detect a meaningful difference when one exists. There are often several alternatives and investigators work with biostatisticians to determine the best design for each application. It is worth noting that the matched design used here can be problematic in that observed differences may only reflect a "placebo" effect. All participants took the assigned medication, but is the observed reduction attributable to the medication or a result of these participation in a study.

## The History and Salient Points of the Documentary Hypothesis

Is there statistical evidence of a reduction in mean total cholesterol in patients after using the new medication for 6 weeks? We will run the test using the five-step approach.

## Mean-Variance Optimization and Modern Portfolio …

There are several approaches that can be used to test hypotheses concerning two independent proportions. Here we present one approach - the chi-square test of independence is an alternative, equivalent, and perhaps more popular approach to the same analysis. Hypothesis testing with the chi-square test is addressed in the third module in this series: BS704_HypothesisTesting-ChiSquare.

## What does the null and alternative hypothesis mean in …

Because the differences are computed by subtracting the cholesterols measured at 6 weeks from the baseline values, positive differences indicate reductions and negative differences indicate increases (e.g., participant 12 increases by 2 units over 6 weeks). The goal here is to test whether there is a statistically significant reduction in cholesterol. Because of the way in which we computed the differences, we want to look for an increase in the mean difference (i.e., a positive reduction). In order to conduct the test, we need to summarize the differences. In this sample, we have