March 25, 2004
Hypothesis Testing
We will cover the normal distribution with known and unknown variance, sample proportions, and difference in two means. We will also cover one-tailed and two-taled tests. Today, we started with the normal distribution with a known mean.
Suppose we know a box of cereal is normally distributed with a standard deviation of 1 and, under the null hypothesis, a mean of 16. We constructed a two-tailed rejection region for a 5% Type I error probability and compared those calculations with a 95% confidence interval. Our rejection region is two-tailed because we are concerned with both means above 16 ounces and means below 16 ounces.
The conclusions reached by two-tailed hypothesis tests and symmetric confidence intervals are very similar because the numbers involved are identical. These are really just two ways of thinking about the same issue.
To determine the Type II error probabilty, we have to consider various values for the mean under the alternative hypothesis.
If these Type II error probabilities are too large, we could increase the sample size.
If we are concerned only about means below 16 ounces, the a one-tailed test is appropriate.
