Introduction

There is always the possibility of making an inference error --- of making the wrong decision about the null hypothesis. We never know for certain if we've made the right decision. However:

The techniques of hypothesis testing allow us to know the probability of making a type I error.

Here is what we do:

We compare the sample mean and the population mean hypothesized under the null hypothesis and decide if they are "significantly different".
• If we decide that they "are significantly different", we reject the null hypothesis:
  

  REJECT:

• If we decide that "are not significantly different" we retain the null hypothesis:
  

  RETAIN:

To do this we must determine:

• What data would be likely if Ho were true,
  and
• What data would be unlikely if Ho were true.

This is done by looking at the distribution of all possible outcomes, if Ho were true.

Since we usually are concerned about the mean we usually look at the Sampling Distribution of Means that we would obtain if Ho were true.

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Example:

We return to the example concerning prenatal exposure to alcohol on birth weight in rats.

We continue to assume that

• The population of rats has a mean birthweight of 18 grams.
• We also assume that the population has a standard deviation of 4.

Usually, such assumptions are untenable, but in some empirical situations we really know this type of information.

We want to know:

• How likely are we to get a particular sample of data if the null hypothesis is true?

We use the Sampling Distribution of Means for these data to come to a decision.

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Now we have to get some data!

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