In a classic study by Cooper and Zubek (1958), maze-dull rats made significantly more errors than maze-bright rats only if they had been reared in: A. isolation. B. an impoverished environment. C. a natural habitat. D. an enriched environment.
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2. Rosenzweig et al. (1972) subjected pairs of rats to live in "impoverished" versus "enriched" surroundings, where each pair of rats was taken from a single litter to ensure genetic similarity. In the enriched environment, rats lived among other rats in large cages and were furnished with new playthings everyday, whereas in the impoverished environment, each rat lived alone in an unfurnished cage. At the end of an experimental period "the rats were sacrificed and their brains removed" and their cortexes weighed, resulting in the following weights in milligrams (partial data are given as presented on pg. 453 of Freedman et al. (1991)): Pair Enriched Impoverished | Pair Enriched Impoverished 1 689 657 | 7 664 600 2 656 623 | 8 647 640 3 668 652 | 9 694 605 4 660 654 | 10 633 635 5 679 658 | 11 653 642 6 663 646 (a) Write down the hypotheses in which the following scientists are interested: i. Rosenzweig wants to know if the enriched environment leads to heavier cortexes. ii. Bennett wants to know if the enriched environment results in lighter cortexes. iii. Diamond wants to know if being in an enriched versus an impoverished environment has any effect on the weights of rat cortexes. (b) Suppose the mean difference (enriched minus impoverished) is 5 milligrams. i. Which scientists could make a Type I error? ii. Which scientists could make a Type II error? (c) Calculate the sample mean and standard deviation of the differences between the cortex weights of the rats in the enriched versus impoverished environments (enriched minus impoverished). (d) Make a QQ plot of the differences between the cortex weights of the rats in the enriched versus impoverished environments (enriched minus impoverished). Comment on whether the differences appear to be Normally distributed. (e) Assuming that the differences in cortex weight follow a Normal distribution, give the value of the test statistic for testing the hypotheses of the scientist in part (a). (f) Assuming that the differences in cortex weight follow a Normal distribution, state, for each scientist in part (a), whether he or she rejects the null hypothesis at the α = 0.05 level. (g) Assuming that the differences in cortex weight follow a Normal distribution, build a 95% confidence interval for the mean difference in cortex weight between rats in an enriched versus an impoverished environment.
Lien L.
Bennett, Krech, and Rosenzweig (1964) suggest that the environment in which an animal grows has a profound effect on brain development. In particular, it is hypothesized that the more enriched the environment, the more developed the cortex of the brain. In one study, laboratory rats were raised in one of two environmental conditions: enriched or isolated. Rats raised in enriched environments had access to toys and other animals. The rats raised in the isolated environment were placed in cages alone in a dimly lit room and did not have access to toys or other animals. Post-mortem, ten rats (five from each condition) were examined and the weight of the cortex (in milligrams) was obtained. Can you conclude that enriched environments increase cortex weight? State the test to be conducted and why: State the null and alternative hypotheses: Find the CV and state the decision rule. Sketch the curve.
Adi S.
Sri K.
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