1. Unit 9: Testing a Claim 9.3A—Significance Test for a Population Mean 1

2. Objectives 9.3A: Perform a significance test Write hypotheses Check conditions Perform the mechanics Make a decision linked in context 2

3. ♥ We ASSUME that the null hypothesis is true ♥ We choose an alpha level ♥ This alpha level is the probability of committing a type 1 error. ♥ A type 1 error is rejecting a null hypothesis when the null is actually true ♥ If alpha = 5%, then 5% of the samples will have results that will lead me to reject the null even though it is true. 3

4. Example: Bolts! A manufacturer of a special bolt requires that this type of bolt have a mean shearing strength in excess of 110 lb. To determine if the manufacturer’s bolts meet the required standards a sample of 35 bolts was obtained and tested. The sample mean was 112.7 lb and the sample standard deviation was 9.62 lb. Use this information to perform an appropriate hypothesis test with a significance level of 0.05. 4

5. Example: The Gem Show! A jeweler is planning on manufacturing gold charms. His design calls for a particular piece to contain 0.08 ounces of gold. The jeweler would like to know if the pieces that he makes contain (on the average) 0.08 ounces of gold. To test to see if the pieces contain 0.08 ounces of gold, he made a sample of 16 of these particular pieces and obtained the following data. 0.0773 0.0779 0.0756 0.0792 0.0777 0.0713 0.0818 0.0802 0.0802 0.0785 0.0764 0.0806 0.0786 0.0776 0.0793 0.0755 Use a level of significance of 0.01 to perform an appropriate hypothesis test. 5

6. A blogger claims that US adults drink an average of five 8-oz glasses of water each day. You think it is less than the blogger claims and take a random sample of 24 adults. Assume that the graph of your sample data shows a mound shape with no outliers. Your sample mean is 4.204 glasses with standard deviation of 1.170. Example: Water? 6

7. Example: Body Temperature I don’t believe that human body temperature really is 98.6°F. To test my theory, I take a random of sample of 130 people and measure their temperature. The sample mean is 98.25°F and the standard deviation is 0.73°F. Is there sufficient evidence to claim that human body temperature is not 98.6°F? 7

8. Computer Output One-Sample T Test of mu = 98.6 vs not = 98.6 N MeanStDev SE Mean 95% CI T P 130 98.2500 0.7300 0.0640 (98.1233, 98.3767) -5.47 0.000 8