Question
a. Platelet Counts of Women. 95% confidence; n = 30, s = 65.2
b. Nicotine in Menthol Cigarettes. 99% confidence; n = 40, s = 0.24mg
Table A-4 Chi Square Distribution Area to the Right of the Critical Value Degrees of 7.879 0,016 2.706 3.84 5.024 0010 0020 0.051 10597 4605 5.99 6.251 7815 11,345 0.216 0.072 0.115 14860 1.064 9.488 1.143 16,750 9.236 11.071 2.833 15.086 1.145 1,610 0.412 16812 8.548 12,592 4,449 1.237 1.635 0676 18475 20.278 14.067 6.013 2833 2.017 21.965 1646 2.180 3.490 13.362 15,507 17535 20.090 16,919 19.023 21666 23589 4.168 14684 1,735 2.088 18307 20483 24209 25.188 15.987 10 2.156 3247 3940 4.865 24725 26,757 17.275 19,675 3.816 4.575 26.217 28.299 12 3074 4,404 5.226 6,304 24,736 27688 29,819 4107 19812 13 29.141 31.319 4,660 6,571 14 15 8547 22.307 24.996 30,578 4601 6.262 28845 32.000 34.267 16 5.142 9312 23.542 26.296 5.812 6908 5697 24,769 27.587 35.718 6408 8672 10.085 10865 25989 28,869 31.526 34,805 37.156 18 7015 8.23 30.144 32 852 36.191 19 6844 10,117 11.65 12443 28.412 31,410 301 7434 8260 9,59 10.85 37,566 13240 29615 32.671 35,479 41.40 10.283 11,59 14.042 30,813 33924 8643 12.338 36,781 42,796 11,689 13.09 35.172 38.076 41.638 10,196 14 848 15.659 33196 36415 30364 10.856 12,401 9886 42.980 3.120 44314 11524 14.61 16.473 11.160 12.198 3.844 15.379 17292 41.923 45.642 11,808 12.879 4,573 6.15 18.114 36,741 40.113 12.46 5.308 18.939 37916 41.337 44.461 48.278 19768 39087 42.557 49,588 52336 13.12 6.047 45,722 4,954 6.791 53,672 46,979 22.164 24433 29.051 51.805 55.758 59,342 27.991 29.707 32357 34.764 37.689 63.167 67 505 71420 76.154 74,397 91.952 51,739 55329 85527 90531 43.275 45,442 48,758 104.215 51.172 57,153 96.578 101.879 112.329 116321 106.629 59 196 61,754 65.647 126 107565 113.145 118.136 124.116 128299 100 70.065 74.222 82,358 135.807 118498 124,342 129561 140,169 Source Donald B.0wen, Handbook of Statistical Tables. Degrees of Freedom Confidence interval or hypothesis test for a standard deviation r or variance a? Goodness-of-fit with k categories Contingency table with rrows and c columns (r- 10 (C Kruskal-Wallis test with k samples
Explanation / Answer
Solution
Back-up Theory
100(1 – ) % confidence interval for 2 is:
{(n - 1)s2/Chi-square (n - 1), /2, (n - 1)s2/Chi-square (n - 1), 1 - /2}
Now, to work out the solution,
Part (a)
Given n = 30, s = 65.2, degrees of freedom for Chi-square distribution is 29. From the Chi-square Table, Chi-square 29, 0.025 = 45.722 and Chi-square 29, 0.975 = 16.047. 95% confidence interval for 2 of Platelet Counts of Women is:
{(29)(65.22)/45.722, (29)(65.22)/16.047} = (2696.2984, 7682.4428)
Taking square roots, 95% confidence interval for of Platelet Counts of Women is: (51.92, 87.65) ANSWER
Part (b)
Given n = 40, s = 0.24mg, degrees of freedom for Chi-square distribution is 39. From the Chi-square Table, Chi-square 39, 0.005 = 66.766 and Chi-square 39, 0.995 = 26.707. 99% confidence interval for 2 of Nicotine in Menthol Cigarettes is
{(39)(0.242)/66.766, (39)(0.242)/26.707} =(0.03785160, 0.09462688).
Taking square roots, 99% confidence interval for of Nicotine in Menthol Cigarettes is
(0.1946, 0.3076) ANSWER
