Reference no: EM132483868
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 (lbs) Weight After (lbs). 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 181.1 180.4 -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. 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.
a. State the null and alternative hypotheses.
b. Explain why the t-distribution is a better choice to use than the z-distribution in this situation.
c. Compute the test statistic. For full credit, be sure to show your work.
d. 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.
e. Using either the p-value or critical value method, make a decision about the null hypothesis.
f. 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.
a. What is the best point estimate for the mean difference between weight after the diet and weight before the diet?
b. Find the margin of error. For full credit, be sure to include the margin of error formula.
c. Construct the confidence interval and summarize the interval in words.
d. Does the confidence interval support your conclusion from the hypothesis test in problem 2? Why or why not?
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