Hypothesis Testing - Duke University
Chapter 23
Hypothesis Testing ? Examples and Case Studies
Copyright ?2005 Brooks/Cole, a division of Thomson Learning, Inc.
23.1 How Hypothesis Tests
Are Reported in the News
1. Determine the null hypothesis and the alternative hypothesis.
2. Collect and summarize the data into a test statistic.
3. Use the test statistic to determine the p-value. 4. The result is statistically significant if the
p-value is less than or equal to the level of significance.
Often media only presents results of step 4.
Copyright ?2005 Brooks/Cole, a division of Thomson Learning, Inc.
2
23.2 Testing Hypotheses About Proportions and Means
If the null and alternative hypotheses are expressed in terms of a population proportion, mean, or difference between two means and if the sample sizes are large ...
... the test statistic is simply the corresponding standardized score computed assuming the null hypothesis is true; and the p-value is found from a table of percentiles for standardized scores.
Copyright ?2005 Brooks/Cole, a division of Thomson Learning, Inc.
3
Example 2: Weight Loss for Diet vs Exercise
Did dieters lose more fat than the exercisers? Diet Only:
sample mean = 5.9 kg sample standard deviation = 4.1 kg sample size = n = 42 standard error = SEM1 = 4.1/ 42 = 0.633
Exercise Only:
sample mean = 4.1 kg sample standard deviation = 3.7 kg sample size = n = 47 standard error = SEM2 = 3.7/ 47 = 0.540
measure of variability = [(0.633)2 + (0.540)2] = 0.83
Copyright ?2005 Brooks/Cole, a division of Thomson Learning, Inc.
4
Example 2: Weight Loss for Diet vs Exercise
Step 1. Determine the null and alternative hypotheses.
Null hypothesis: No difference in average fat lost in population for two methods. Population mean difference is zero. Alternative hypothesis: There is a difference in average fat lost in population for two methods. Population mean difference is not zero.
Step 2. Collect and summarize data into a test statistic.
The sample mean difference = 5.9 ? 4.1 = 1.8 kg and the standard error of the difference is 0.83. So the test statistic: z = 1.8 ? 0 = 2.17
0.83
Copyright ?2005 Brooks/Cole, a division of Thomson Learning, Inc.
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