Question

2. Calls for primary care providers (PCP’s) to offer obese patients behavioral weight-loss counseling have not been accompanied by adequate guidance on how such care could be delivered. A randomized trial was conducted to compare weight loss during a 2-year period in response to two lifestyle interventions, both delivered by PCP’s in collaboration with auxiliary health professionals (lifestyle coaches) in their practices. The investigators randomly assigned 259 obese adults to one of two types of intervention: usual care or enhanced lifestyle counseling, to potentially increase weight loss. Usual care consisted of quarterly PCP visits that included education about weight management. Enhanced lifestyle counseling consisted of (1) quarterly PCP visits, (2) brief monthly sessions with lifestyle coaches who instructed participants about behavioral weight control, and (3) meal replacements or weight-loss medication. The response variable Y is weight loss at 24 months, expressed as a percentage of initial weight. That is, Y is the weight loss achieved by the patient after 24 months of participation expressed as a percentage of the patient’s initial weight. Since the raw data are not available, we will assume that the assumptions needed to justify the application of two–sample Student’s t methods are valid.

a) Clearly define two relevant population means, µ1 and µ2, with the subscript 1 indicating “usual care” and the subscript 2 indicating “enhanced lifestyle counseling”.

b) State what you believe to be an appropriate research hypothesis relating µ1 to µ2. Provide a clear and complete statement of this hypothesis in words in the context of this problem and explain why your hypothesis is appropriate. Note that for the computations I used zero as the boundary between the null and research hypotheses.

c) Perform a hypothesis test to determine whether the data support your research hypothesis. Provide the relevant P–value and a complete discussion in the context of this problem. d) Provide a complete discussion of the 95% confidence interval estimate for µ1 −µ2 in the context of this problem.

usual care: n = 130, Y 1 = 1.6, S1 = 6.8410

enhanced liefstyle counseling: n = 129, Y 2 = 4.7, S2 = 6.8147

Test: t value = −3.65, (Two–sided) Pr > |t| = .0004, (One–sided) Pr < t = .0002,

95% confidence limits for the mean difference: −4.771 ≤ µ1 − µ2 ≤ −1.429

Answer 1

Here we believe that the average of the “enhanced lifestyle counseling” is more than “usual care” , but we want test the claim,

Ho: The both counselling have same effect on weight loss.

vs H1: The average of the “enhanced lifestyle counseling” is more than “usual care”

Usual care consisted of quarterly PCP visits that included education about weight management and Enhanced lifestyle counseling consisted of (1) quarterly PCP visits, (2) brief monthly sessions with lifestyle coaches who instructed participants about behavioral weight control, and (3) meal replacements or weight-loss medication one and all Enhanced lifestyle counseling more than usual care so the expectation is high from the Enhanced lifestyle counseling.

Therefore we will use here  two–sample Student’s t-test, because the both samples are independent and population variance is unknown.

Here the p-value(one sided) = 0.0002 which is less than 5% level of significance, we may reject Ho and conclude that The average of the “enhanced lifestyle counseling” is more than “usual care”.

95% confidence limits for the mean difference: −4.771 ≤ µ1 − µ2 ≤ −1.429

Here the diffrerence in µ1 − µ2= 0 is not invoved in the confidence interval therfore we may conclude that the difference in the average of the “enhanced lifestyle counseling” is not equal to “usual care.