Are the brains of left-handed people anatomically different? To investigate this question, a neuroscientist conducted postmortem brain examinations in 42 people. Each person had been evaluated before death for hand preference and categorized as consistently right handed (CRH) or mixed-handed (MH).The table shows the results on the area of the anterior half of the corpus callosum (the structure that links the left and right hemispheres of the brain).32 The MS(within) from the ANOVA was 2,498.

(a) The difference between MH and CRH is 56 mm2 for males and 32 mm2 for females. Is this sufficient evidence to conclude that the corresponding population difference is greater for males than for females? Test an appropriate hypothesis. (Use a non directional alternative and let α = 0.10.)
(b) As an overall measure of the difference between MH and CRH, one can consider the quantity 0.5(μ1 - μ2) + 0.5(μ3 - μ4). Construct a 95% confidence interval for this quantity. (This is a sex-adjusted comparison of MH and CRH, where the reference population is 50% male and 50% female.)

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Area (mm2 Group Mean SD 42348 367 49 1 Males: MH Males:CRH 3. Females: MH 377 63 10 Females: CRH 345 43 20