Question

9. In a study of the effectiveness of weight-loss programs, 47 subjects who were at least 20% overweight took part in a group support program for 10 weeks. Private weighings determined each subject's weight at the beginning of the program and 6 months after the program's end. The paired I test was used to assess the significance of the average weight loss. The paper reporting the study said, "The subjects lost a significant amount of weight over time, R46-4.68, P0.01. (a) What hypotheses were tested in this study? Be sure to define any parameters you use (b) Discuss whether each of the required conditions for using the paired/ test is satisfied in this study. (c) The paper follows the tradition of reporting significance only at fixed levels such as α-0.01. In fact the results are more significant than < 0.01" suggests. What is the P.value of this nest? (d) Explain to someone who knows no statistics but is interested in weight-loss programs what the practical conclusion is

Answer 1

9)

a) We want to test Ho: μ = 0, Ha: μ ≠ 0 where μ = mean weight loss

b)

SRS – The subjects were probably not a random sample, hopefully they are representative of a larger population

Normality – sample size is large enough to assume normality (n>30)

Independent – The population is easily greater than 10 * 47

c) Since test statistics value is t = 4.68 for df = 46 so p-value of the test is 0.00026. P-value is less than 0.05 and also from 0.10. So we reject the null hypotheses at 0.05 and 0.10 level of significance. That is result is significant at 0.05 and 0.10 levels of significance.

d)

Result t(46)=4.68, p < 0.01 shows that p value is less than 0.01, so we reject the null hypothesis at 0.01 level of significance.

According to test, the result are significant. That is weight loss program is effective.