# The steps to create a hypothesis are:

The ability to weigh various isotopes, at increasing levels of precision, with mass spectrometers has provided a gold mine of data. Scientists are continually inventing new methods and ways to use them, new questions are asked and answered, and some examples of methods and findings follow.

## Five Steps in a Hypothesis Test

### Next: This page will contain examples of the following:

How likely it is to observe a sample mean of 192.1 or higher when the true population mean is 191 (i.e., if the null hypothesis is true)? We can again compute this probability using the Central Limit Theorem. Specifically,

### Hypothesis Testing - Analysis of Variance (ANOVA)

(Notice that we use the sample standard deviation in computing the Z score. This is generally an appropriate substitution as long as the sample size is large, n __>__ 30. Thus, there is less than a 1% probability of observing a sample mean as large as 197.1 when the true population mean is 191. Do you think that the null hypothesis is likely true? Based on how unlikely it is to observe a sample mean of 197.1 under the null hypothesis (i.e.,

## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

The test statistic is a single number that summarizes the sample information. An example of a test statistic is the Z statistic computed as follows:

## State the null and an appropriate alternal hypothesis. 5.

Analysis of data from a matched pairs experiment compares the two measurementsby subtracting one from the other and basing test hypotheses upon the differences.

## 1. Testing of hypothesis on the variance of two normal populations.

The null hypothesis in ANOVA is always that there is no difference in means. The research or alternative hypothesis is always that the means are not all equal and is usually written in words rather than in mathematical symbols. The research hypothesis captures any difference in means and includes, for example, the situation where all four means are unequal, where one is different from the other three, where two are different, and so on. The alternative hypothesis, as shown above, capture all possible situations other than equality of all means specified in the null hypothesis.

## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

The exact form of the research hypothesis depends on the investigator's belief about the parameter of interest and whether it has possibly increased, decreased or is different from the null value. The research hypothesis is set up by the investigator before any data are collected.