## Null and Alternative Hypotheses for a Mean

This proce- dure can be viewed as a test of the hypothesis p = .05 against the alternative p > .05, p being the probability that the machine turns out a defective item.

ANOVA is a test that provides a global assessment of a statistical difference in more than two independent means. In this example, we find that there is a statistically significant difference in mean weight loss among the four diets considered. In addition to reporting the results of the statistical test of hypothesis (i.e., that there is a statistically significant difference in mean weight losses at α=0.05), investigators should also report the observed sample means to facilitate interpretation of the results. In this example, participants in the low calorie diet lost an average of 6.6 pounds over 8 weeks, as compared to 3.0 and 3.4 pounds in the low fat and low carbohydrate groups, respectively. Participants in the control group lost an average of 1.2 pounds which could be called the placebo effect because these participants were not participating in an active arm of the trial specifically targeted for weight loss. Are the observed weight losses clinically meaningful?

## The hypotheses of interest in an ANOVA are as follows:

Type I error is the probability of rejecting a true nullhypothesis, that is, making the error of claiming that there is asignificant difference between two populations when no such differenceexists.

## For the one sample mean, the hypothesis ..

In one sample tests for a dichotomous outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data. Specifically, we compute the sample size (n) and the sample proportion which is computed by taking the ratio of the number of successes to the sample size,

## 10/31/2005 · Hypothesis Testing - Population Mean ..

Hypothesis testing applications with a dichotomous outcome variable in a single population are also performed according to the five-step procedure. Similar to tests for means, a key component is setting up the null and research hypotheses. The objective is to compare the proportion of successes in a single population to a known proportion (p_{0}). That known proportion is generally derived from another study or report and is sometimes called a historical control. It is important in setting up the hypotheses in a one sample test that the proportion specified in the null hypothesis is a fair and reasonable comparator.

## hypothesis testing- small sample with one population mean

Below is an exercise that will graphically show how the area under thethe t-distrubution that lies beyond the critical t-value changes asthe hypotheses change from one-tailed to two tailed, and as changes aremade to the risk of making a Type I error.

## Hypothesis Test for a Population Mean (1 of 5) | …

Instead, the researcher will usually enter the data into computer anduse statistical software that computes the observed t-value andprovides a probability of the observed t-value occurring assuming thenull hypothesis is true.

## In “Hypothesis Test for a Population Mean,” we learn to ..

A study is designed to test whether there is a difference in mean daily calcium intake in adults with normal bone density, adults with osteopenia (a low bone density which may lead to osteoporosis) and adults with osteoporosis. Adults 60 years of age with normal bone density, osteopenia and osteoporosis are selected at random from hospital records and invited to participate in the study. Each participant's daily calcium intake is measured based on reported food intake and supplements. The data are shown below.