A weight loss center has found that 71% of its participantslose weight. The cent

Question

A weight loss center has found that 71% of its participantslose weight. The center's director decides to test a new weightloss strategy on a random sample of 125 participants and finds that95 of those participants lose weight. Is the new strategy animprovement and should the center adopt the new strategy? Write theappropriate hypotheses (in words and also using correct statisticalnotation) with alpha = 0.01, find the test statistic, find thep-value, and state your conclusion in the context of theproblem. A) Test z = 1.23; P-value = 0.1236. The improvement is notstatistically significant, so the center should adopt the newstrategy. B) Test z = 1.23; P-value = 0.0618. The improvement is notstatistically significant, so the center should not adopt the newstrategy. C) Test z = 1.23; P-value = 0.1093. The improvement is notstatistically significant, so the center should not adopt the newstrategy. D) Test z = 1.23; P-value = 0.1093. The improvement isstatistically significant, so the center should adopt the newstrategy. E) Test z = 1.23; P-value = 0.0618. The improvment isstatistically significant, so the center should adopt the newstrategy. A weight loss center has found that 71% of its participantslose weight. The center's director decides to test a new weightloss strategy on a random sample of 125 participants and finds that95 of those participants lose weight. Is the new strategy animprovement and should the center adopt the new strategy? Write theappropriate hypotheses (in words and also using correct statisticalnotation) with alpha = 0.01, find the test statistic, find thep-value, and state your conclusion in the context of theproblem. A) Test z = 1.23; P-value = 0.1236. The improvement is notstatistically significant, so the center should adopt the newstrategy. B) Test z = 1.23; P-value = 0.0618. The improvement is notstatistically significant, so the center should not adopt the newstrategy. C) Test z = 1.23; P-value = 0.1093. The improvement is notstatistically significant, so the center should not adopt the newstrategy. D) Test z = 1.23; P-value = 0.1093. The improvement isstatistically significant, so the center should adopt the newstrategy. E) Test z = 1.23; P-value = 0.0618. The improvment isstatistically significant, so the center should adopt the newstrategy.

Explanation / Answer

Given p=0.71, n=125, phat=95/125=0.76 =0.01, Z(0.005)=2.58 (check normal table) The test hypothesis is Ho:p0.71 The test statistic is Z=(phat - p)/p*(1-p)/n =(0.76-0.71)/sqrt(0.71*(1-0.71)/125) =1.23 The p-value is P(Z>1.23)= 0.1093 (check normal table) Since p-value is greater than =0.01, we do not reject Ho. Answer: C) Test z = 1.23; P-value = 0.1093. The improvement is notstatistically significant, so the center should not adopt the newstrategy.

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