4.(a) (i) no: the sample sizen(number of flowers inthe plot) is not pre-specified.(ii) yes(iii) no: flies in the same family are likely to havethe same eye color, so the individuals in the sam-ple are not independent.It is okay to see thisas a non-constant probability of having red eyes:those probabilities are unknown (families are ran-domly sampled) but are probably different acrossdifferent families.(b) (i)H0:p=.5 vsHA:p > .5(ii) .0985 (iii) mean 49, sd 4.95 (iv)≈.0078Note: A real experiment done by schoolchildrenreachedn= 9821 and observedy= 6101 ! Seeourworld.compuserve.com/homepages/rajm/ssrsum.htm5.(a) mean= 8 (center of symmetry). We know thereis 95% of the area whithin±1.96*sd of the mean,with 0.025 on each side. This is the area between≈7 and 9. Therefore 2 sd≈9-8 and sd≈0.5.(b) z=0.52 so the value is 0.52 sd above from themean: 8mm + 0.52 * 0.5 = 8.26 mm.(c) (i) forn= 1, (ii) forn= 8, (iii) forn= 2: theshape looks more like a bell curve whennis large.Also, the variability of the sample mean decreasesasnincreases (compare the scales).
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