A weight loss program claims it will help people lose weight quickly. A researcher wants to test this claim. He randomly selects thirteen women who desire to lose 30 or more pounds. He records the weight of each subject. Each subject follows the weight loss program for four weeks. The researcher then measures each subjects weight at the end of the four weeks.The table below shows the results. Is there evidence that the diet helps women lose weight after 4 weeks?Use a significance level of =0.05.

Weight before diet (kg)81.5 125.3 93.2 89.1 105.2 130.5 122.3 95.7 143.2 145.5 138.7 92.3 96.2

Weight after 4 weeks (kg)78.5 125 91.8 85.0 98.0 129.5 115.5 95.5 135.9 143.7 142.0 87.5 92.0

a)A paired t-test requires that the samples be dependent. Is that condition met for this problem? Why or why not.

b)Check that the sample meets the other necessary conditions to perform a t-test.

c)How did you check that your data meets the nearly normal condition? What did you need to determine in order to conclude the sample is nearly normal?

d)State the hypotheses in symbols. Be careful! Your hypotheses will depend on how you set up L3.

e)Use your calculator to perform a t-test on L3 = L1 L2and report the test statistic and p-value. Be sure to write which list you entered into L1 and which list you entered for L2, and, as usual, write out what you entered in your calculator.

f)Write a full conclusion for this test in the context of the problem.

g)Find a 90% confidence interval for the difference in weight of the subjects before and after being on the diet. Be sure to write out what you entered in your calculator. Do NOT do this by hand but instead use the correct test command in your calculator.

h)Interpret the confidence interval in the context of this problem.

i)Does this confidence interval support your conclusion in part (f)? Explain.