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# 4a i no the sample size n number of flowers in the

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4.(a) (i) no: the sample size n (number of flowers in the plot) is not pre-specified. (ii) yes (iii) no: flies in the same family are likely to have the same eye color, so the individuals in the sam- ple are not independent. It is okay to see this as a non-constant probability of having red eyes: those probabilities are unknown (families are ran- domly sampled) but are probably different across different families. (b) (i) H 0 : p = . 5 vs H A : p > . 5 (ii) .0985 (iii) mean 49, sd 4.95 (iv) . 0078 Note: A real experiment done by schoolchildren reached n = 9821 and observed y = 6101 ! See ourworld.compuserve.com/homepages/rajm/ ssrsum.htm 5.(a) mean= 8 (center of symmetry). We know there is 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 the mean: 8mm + 0.52 * 0.5 = 8.26 mm. (c) (i) for n = 1, (ii) for n = 8, (iii) for n = 2: the shape looks more like a bell curve when n is large. Also, the variability of the sample mean decreases as n increases (compare the scales).
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