2. Diets. Developers of diets like to advertise that their diets produce signifi

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2. Diets. Developers of diets like to advertise that their diets produce significant weight loss results. A new diet has been developed and several studies were done to investigate the effectiveness of the diet. In each study the average number of pounds lost was of interest, and researchers would like to show that dieters lost a significant amount of weight. (a) Identify µ in this scenario. (Choose One) • Average number of pounds lost by all people in the sample. • True average weight of all people in the population. • True average number of pounds lost by all people in the population. • Average weight of all people in the sample. 1

(b) Identify the appropriate null and the alternative hypotheses to test the researchers’ claim. H0 : Ha :

(c) Suppose that an average weight loss of 1 pound (x = 1) and standard deviation of s = 7 pounds were found in each of the following scenarios. Further, assume weight loss is normally distributed. For each case, compute the test statistic, find the approximate pvalue and make a decision about the null hypothesis using an = 0.05 level of significance. Round t-statistics to two decimals. i.

Scenario 1: a sample of size n = 10 A. t = and df = B. The p-value corresponding to the correct test statistic is 0.331. This p-value suggests against the null hypothesis. (Choose One) • Little or no evidence • Weak evidence • Moderately strong evidence • Strong evidence • Extremely strong evidence C. Decision: • Reject the null hypothesis because the p-value . • Reject the null hypothesis because the p-value > . • Fail to reject the null hypothesis because the p-value . • Fail to reject the null hypothesis because the p-value > .

ii. Scenario 2: a sample of size n = 120 A. t = and df = B. The p-value corresponding to the correct test statistic is 0.0601. This p-value suggests against the null hypothesis. (Choose One) • Little or no evidence • Weak evidence • Moderately strong evidence • Strong evidence • Extremely strong evidence C. Decision: • Reject the null hypothesis because the p-value . • Reject the null hypothesis because the p-value > . • Fail to reject the null hypothesis because the p-value . • Fail to reject the null hypothesis because the p-value > .

2 iii. Scenario 3: a sample of size n = 1050 A. t = and df = B. The p-value corresponding to the correct test statistic is 0.000002. This p-value suggests against the null hypothesis. (Choose One) • Little or no evidence • Weak evidence • Moderately strong evidence • Strong evidence • Extremely strong evidence C. Decision: • Reject the null hypothesis because the p-value . • Reject the null hypothesis because the p-value > . • Fail to reject the null hypothesis because the p-value . • Fail to reject the null hypothesis because the p-value > .

D. (FREE RESPONSE) A weight loss of one pound is found to be statistically significant. The researchers share their results with the public claiming that their diet produces meaningful, significant weight loss. Do you agree? Explain your answer.

Explanation / Answer

2. (a) True average weight of all people in the population.

(b) H0 : a - b = 0 vs. H1 : a - b > 0 where a = after and b = before.

(c) i) Mean = 1, SD = 7, n = 10 then  t = 0.4518 and df = 9.

This p-value suggests against the null hypothesis - Strong evidence.

Fail to reject the null hypothesis because the p-value > .

ii) Mean = 1, SD = 7, n = 120 then  t = 1.5649 and df = 119.

This p-value suggests against the null hypothesis - Moderately strong evidence.

Fail to reject the null hypothesis because the p-value > .

iii) Mean = 1, SD = 7, n = 1050 then   t = 4.6291 and df = 1049.

This p-value suggests against the null hypothesis - Extremely strong evidence.

Reject the null hypothesis because the p-value .

d) I dont agree as when sample size increases power of test also increases but it can also lead to a wrong conclusion shown in the above scenarios.

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