1. AP Statistics Chapter 24 Notes “Comparing Two Sample Means”

2. New Formulas ***USE THE CALCULATOR FOR DEGREES OF FREEDOM*** (n – 1 only applies for 1-sample means n – 2 can be an approximate estimate)

3. Hypothesis Testing  A hypothesis test for the difference in the means of two independent groups tests the null hypothesis: o The alternate hypothesis is one of the following:

4. Example – with stats  Is there a difference between the resting pulse rates of males and females? A researcher collected data from a random sample of US men and women and found that the average resting pulse rate among the 280 men sampled was 72.75 beats per minute with a standard deviation of 5.4. The 240 women sampled had an average resting pulse rate of 70.63 beats per minute with a standard deviation of 7.7. Is this sufficient evidence to say that there is a difference between the resting pulse rates of males and females?

5. Step-by-Step Solution Process  State the hypotheses  Check the conditions Random samples – given information Independent events – the resting pulse rate of one person is not influenced by the resting pulse rate of another person The population of all US men must be at least 2800 men and the population of all US women must be at least 2400 women. Since the sample sizes are over 40, we do not have to check a histogram of each set to make sure it is unimodal and roughly symmetric. We can proceed on with the testing.

6. Step-by-Step Solution Process  Perform a two sample t test (Stat, Tests, #4)  State your conclusion

7. Confidence Interval (Stat, Tests, #0)  Find the 95% confidence interval for the difference between the mean resting pulse rates for the men and women.  Interpret this interval. Based on this sample, we are 95% confident that the mean resting pulse rate for US men is between _________ and __________ _____________ than the mean resting pulse rate for US women.  Does it support your conclusion? Why?