Question

Week 10 Assessment

Background

Researchers are interested in determining if a new diet program is effective at helping people lose weight. In a pilot study, the researchers collect a random sample of 10 subjects and measure their weight before beginning the diet, then again after one month on the diet program.

Data

The following table summarizes the information collected:

Patient	Weight Before (in lb)	Weight After (in lb)	Difference (After minus Before)
Subject #1	207	202	-5
Subject #2	179	180	1
Subject #3	172	172	0
Subject #4	180	181	1
Subject #5	197	196	-1
Subject #6	195	193	-2
Subject #7	182	184	2
Subject #8	168	166	-2
Subject #9	157	157	0
Subject #10	174	173	-1
Mean	181.1	183.4	-0.7
Standard Deviation	14.9	14.0	2.0

NOTE: A positive difference means that the patient’s weight after the program was actually higher than their weight before the program.

Problems

Problem 1. (2 points) Based on an analysis of the information in the table, do you feel that this study provides convincing evidence that the diet is, on average, helping patients lose weight? Explain why or why not.

Problem 2. Weight loss occurs when the difference between ending weight and starting weight is negative. To determine if a weight loss has occurred, we could conduct a hypothesis test to see if the average difference is negative, using a 5% significance level.

1. (2 points) State the null and alternative hypotheses.
2. (2 points) Explain why the t-distribution is a better choice to use than the z-distribution in this situation.
3. (2 points) Compute the test statistic. For full credit, be sure to show your work.
4. (2 points) Compute the p-value or the critical value (depending on the method you prefer). Either way, be sure to show your work by drawing a sketch.
5. (2 points) Using either the p-value or critical value method, make a decision about the null hypothesis.
6. (1 point) Based on the results of the hypothesis test, is there convincing evidence that this diet is helping patients lose weight?

Problem 3. We now wish to construct a 98% confidence interval for the mean difference between weight after the diet and weight before the diet.

1. (1 point) What is the best point estimate for the mean difference between weight after the diet and weight before the diet?
2. (2 points) Find the margin of error. For full credit, be sure to include the margin of error formula.
3. (2 points) Construct the confidence interval and summarize the interval in words.
4. (2 points) Does the confidence interval support your conclusion from the hypothesis test in problem 2? Why or why not?

Answer 1