Do left-handed people live shorter lives than right-handed people? A study of th
ID: 3296007 • Letter: D
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Do left-handed people live shorter lives than right-handed people? A study of this question examined a sample of 949 death records and contacted next of kin to determine handedness. Note that there are many possible definitions of "left-handed." The researchers examined the effects of different definitions on the results of their analysis and found that their conclusions were not sensitive to the exact definition used. For the results presented here, people were defined to be right-handed if they wrote, drew, and threw a ball with the right hand. All others were defined to be left-handed. People were classified by gender (female or male) and handedness (left or right), and a 2 times 2 ANOVA was run with the age at death as the response variable. The F statistics were 22.36 (handedness), 37.44 (gender), and 2.10 (interaction). The following marginal mean ages at death (in years) were reported: 77.39 (females), 71.32 (males), 75.00 (right-handed), and 66.03 (left-handed). (a) For each of the F statistics given, find the degrees of freedom and an approximate P-value. Round your p-values to 3 decimal places. Handedness Degrees of Freedom Handedness P-Value Gender Degrees of Freedom Gender P-Value Interaction Degrees of Freedom Interaction P-Value What can you conclude from this study? Choose all that apply. Right handed people live about 9 years longer than left-handed people. Right handed people live about 6 years longer than left-handed people. Women live about 9 years longer than men. Handedness affects both genders in the same way (there is no interaction). Handedness affects the genders differently (there is an interaction). Women live about 6 years longer than men.Explanation / Answer
a. From information given main effect handedness has two levels-left and right, as well as main effect gender has two levels male and female. Main effect handedness has (a-1)=(2-1)=1 degree of freedom. Main effect gender has (b-1)=(2-1)=1 degree of freedom. Interaction (handedness*gender) has (a-1)(b-1)=1*1=1 degree of freedom. Error degrees of freedom is ab(r-1), where r is number of measurements for each pair of levels of independent variables a and b. It is known that n=abr, thus, r=n/ab=948/(2*2)=237. Thus, Error(df)=4*236=944.
Use technology to obtain the p value corresponding to given F values.
Handedness degrees of freedom is 1, 944 and p value:0.000
Gender degrees of freedom is 1,944 and p value: 0.000
Interaction degrees of freedom is 1, 944 and p value: 0.148
The interaction test results into p value larger than alpha=0.05. Therefore, there is no interaction between handedness and gender. Option 4 is applicable. Once, it is found that there is no interaction, conduct tests for main effects handedness and gender. Both the results are significant (p value for both handedness and gender are much lower than alpha=0.05). Thus conclude that left handed people live shorter lives than left handed. Option 1 and 2 are therefore, right. As far as significant effect of gender on year lived is concerned, the hypothesis is not available, thus result is inconclusive.
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