1. State the Null and the Alternative Hypothesis

Session Review Leader: Luyun Statistics 226 Course: Stat 226 Supplemental Instruction Instructor: Anna Peterson Iowa State University Date: 4/3/16

Example1: developing a new diet (to lose weight) and measure the # of lbs lost. A random sample of 36 people on the diet yielded an average # of pounds lost of 2.9 lbs with a standard deviation of 5.7 lbs. is there sufficient evidence in the data to conclude that the diet is effective? Conduct an appropriate test of hypothesis at the α = 0.01 level of significance.

1. State the null and the alternative hypothesis.

2. What is the value of test statistic? Show your work.

3. Using the JMP output below, answer the following questions:

Test Mean: Hypothesized value 0 Actual estimate 2.9 DF 35 Std Dev 5.7

T test Test statistic 3.0526 Prob > |t| 0.0043* Prob > t 0.0022* Prob < t 0.9978

(a) Based on the alternative hypothesis, what is the appropriate p-value?

(b) Provide an interpretation for this p-value in the context of the data.

(c) Make a conclusion about Ho based on your P-value and the given level of significance.

Example2: a random sample of 30 Stat 226 students yielded an average number 1.86 caffeinated drinks per day and a standard deviation of 1.28. Is there evidence that the average number of caffeinated drinks per day for all Stat 226 students is different from 1.57 Test this claim at the α = 0.10 level of significance.

1060 Hixson-Lied Student Success Center v 515-294-6624 v [email protected] v http://www.si.iastate.edu 1. State the null and the alternative hypothesis.

2. What is the value of test statistic? Show your work.

3. Using the JMP output below, answer the following questions:

Test Mean: Hypothesized value 1.5 Actual estimate 1.86 DF 29 Std Dev 1.28

T test Test statistic 1.5405 Prob > |t| 0.1343* Prob > t 0.0671* Prob < t 0.9329

(d) Based on the alternative hypothesis, what is the appropriate p-value?

(e) Provide an interpretation for this p-value in the context of the data.

(f) Make a conclusion about Ho based on your P-value and the given level of significance.

Example 3: brand managers become concerned if they discover that customers are aging and gradually moving out of the high-spending age groups. For example, the average Cadillac buyer is 55 or older past the prime middle years that typically are associated with more spending. Part of the importance to Cadillac of the success of the Escalade model has been its ability to draw in younger customers. if a sample of 50 Escalade purchasers has average age 47.22 (with standard deviation 27.72), is this compelling evidence (at the 0.05 level ) that Escalade buyers are younger on average than the typical Cadillac buyer?

Test Mean: Hypothesized value 55 Actual estimate 47.22 DF 49 Std Dev 27.72

T test Test statistic -1.9846 Prob > |t| 0.0528 Prob > t 0.9736 Prob < t 0.0264