13. Investigators gave caffeine to fruit flies to see if it affected their rest.

Question

13. Investigators gave caffeine to fruit flies to see if it affected their rest. The four treatments were a control, a low caffeine dose of 1 mg/ml of blood, a medium dose of 3 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest measured over a 24-hour period were recorded. The data follow Treatment Control Low dose Medium dose High dose Minutes of rest 450 413 466 422 421453 364 330 418 435 419 389 Assume the data are four independent SRSs, one from each of the four populations of caffeine levels, and that the distribution of the yields is Normal. A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups. One-way ANOVA: Rest Versus Caffeine MS Source Caffeine 11976 rror 538.75 ota Level Contro1 3 427.00 20.07 Low Medium 3 431.00 19.08 High N Mean StDev 3 441.00 22.61 3 361.00 29.61 The conclusion that you would draw from this test is to: A) accept the null hypothesis; all of the groups have the same mean. B) fail to reject the null hypothesis; there is no evidence to suggest that the groups have different means. reject the null hypothesis; all of the group means are different from one another reject the null hypothesis; at least one of the groups has a mean that is different than the other means. C) D)

Explanation / Answer

THe ANOVA table is given below

Here dF = k - 1 = 4 - 1= 3

SS = 11976

MSW = SSW/dF(Wi) = 11976/3 = 3992

dF = 4 * (3-1) = 8

MSE = 538.75

SSE = 538.75 * 8 = 4310

F = MSW/MSE = 3992/538.75 = 7.4097

F(critical) = F (0.05, 3,8) = 4.066

Here F > F(critical)  

so we can reject the null hypothesis ; at least one of the groups has a mean that is different than the other means.

Option D is correct.

ANOVA Source of Variation SS df MS F P-value Between Groups 11976 3 3992 7.409745 0.010714 Within Groups 4310 8 538.75 Total 16286 11

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