# Problem 8 4 points each as part of a study of the

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Problem 8 (4 points each). As part of a study of the swimming speed of sharks, a random sample of 18 lemon sharks ( Triakis semifasciata ) were observed in a laboratory sea tunnel. Body lengths (cm) and maximum sustainable swimming speeds (“MSSS,” reported in body lengths per second) were measured for each shark. Computer output from a regression with y = MSSS and x = body length gave ࠵?࠵?࠵?࠵? = 1 . 8928955 0 . 0104278 × ࠵?࠵?࠵?࠵?࠵? . Some other useful summary statistics ࠵? = 62 . 61 ; MSE = ࠵? ! ! = 0 . 074 ; S !! = 12100 . 04 . a) You wish to test the hypothesis that the population slope is different than zero. The correct hypotheses are: are: A) ࠵? ! : ࠵? = 0 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ! : ࠵? > 0 B) ࠵? ! : ࠵? < 0 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ! : ࠵? > 0 C) ࠵? ! : ࠵? = 0 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ! : ࠵? 0 D) ࠵? ! : ࠵? = 0 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ! : ࠵? 0
b) The correct test statistic for the test in (a) above is:
c) Using ࠵? = 0 . 01 , what is the critical t -score that separates the rejection region for the test of the regression slope in part (a)? d) At the 1% significance level, in the context of the problem , what do you conclude about the hypothesis test of the slope parameter? e) On average, the predicted length of a shark when the swimming speed is 1.50 body lengths/s is
7 Problem 9 (4 points each). Researchers believe there will be differences in oxygen consumption rates for Acmaea scabra , a species of limpet, when the limpets are exposed to differing concentrations of seawater. To test their claim, three experimental rocky tide pool environments were set up with one of three seawater concentrations (50%, 75% and 100%). Four limpets were placed in each tide pool and their oxygen consumption was measured over a period of eight hours. Oxygen consumption was measured in microliters O ! / mg dry body weight/min at 22 ! a) The null and alternative hypotheses for testing the researcher’s claim are I. ࠵? ! : ࠵? !" = ࠵? !" = ࠵? !"" versus ࠵? ! : ࠵? !" ࠵? !" ࠵? !"" II. ࠵? ! : ࠵? !" = ࠵? !" = ࠵? !"" versus ࠵? ! : ࠵? !" > ࠵? !" > ࠵? !"" III. ࠵? ! : ࠵? !" = ࠵? !" = ࠵? !"" versus ࠵? ! : the means are not equal for at least one pair b) Complete the ANOVA table below (all white spaces) used to determine if there are differences in mean oxygen consumption rates at the three tested seawater levels. C. ANOVA Table Source of Variation SS df MS F p -­‐value Concentration 0.001 < p < 0.01 Error 35.72 Total 137.9 c) Using ࠵? = 0 . 01 and only one sentence, provide a conclusion for the one-way ANOVA, in the context of the problem.