Question

Use the information below to answer the CANCER SURVIVAL questions that follow. Data originally from DASL http://lib.stat.cmu.edu/DASL/Datafiles/CancerSurvival.html . Some bronchial cancer patients had the following survival times (in days) after receiving a certain treatment: 20, 37, 63, 64, 72, 81, 138, 151, 155, 166, 166, 223, 245, 246, 450, 459. (The second instance of "166" is not a mistake.) Do these numbers suggest that the average survival time, for all bronchial cancer patients who receive that treatment, is significantly different from 200 days?

Answer 1

Survival times (in days) of some bronchial cancer patients be x as random variable. Data! 20, 37, 63, 64, 72, 81, 138, 151 , 155, 166, 166, 223,245, 246, 450, 459 XEX 2736 16 171 in S? Il ex²_nX²) = 1 + 726012– 16 X1712) 15 s? S n-1 17210.4 2.131.1884141 The Null and alternative hypothesis H = 200 qiil The average survival time is 200 days. He : Hi : M 7 200 ta X-M The test statistic is 171-200 0.88 112 Slun 131.188 / NT6 The degrees of freedom on t is 15. Critical value: to P-value = 2P(+15 (-0.88) = 2P( 415 > 0.88) = 2 x 0.1964 0.3928 At 1% 5% and 10% we do not reject Ho. Hence we support the claim that the average survival time for all bronchial cancer patients who recieve the treatment is is significantly different from 200 days. P-value -

Probabilities for the Standard Normal distribution The distribution function is denoted by (x), and the probability density function is denoted by °(x). 1 - (x) 0 (x) = { * °(t)dt = √r si e-%22 di 0 х 0(x) °(x) Þ(x) °(x) 0(x) 0.00 0.50000 0.40 0.65542 0.80 0.78814 1.20 0.88493 1.60 0.94520 0.01 0.50399 0.41 0.65910 0.81 0.79103 1.21 0.88686 1.61 0.94630 0.02 0.50798 0.42 0.66276 0.82 0.79389 1.22 0.88877 1.62 0.94738 0.03 0.51197 0.43 0.66640 0.83 0.79673 1.23 0.89065 1.63 0.94845 0.04 0.51595 0.44 0.67003 0.84 0.79955 1.24 0.89251 1.64 0.94950 0.05 0.51994 0.45 0.67364 0.85 0.80234 1.25 0.89435 1.65 0.95053 0.06 0.52392 0.46 0.67724 0.36 0.80511 1.26 0.89617 1.66 0.95154 0.07 0.52790 0.47 0.68082 0.87 0.80785 1.27 0.89796 1.67 0.95254 0.08 0.53188 0.48 0.68439 0.38 0.81057 1.28 0.89973 1.68 0.95352 0.09 0.53586 0.49 0.68793 0.89 0.81327 1.29 0.90147 1.69 0.95449 0.10 0.53983 0.50 0.69 146 0.90 0.81594 1.30 0.90320 1.70 0.95543 0.11 0.54380 0.51 0.69497 0.91 0.81859 1.31 0.90490 1.71 0.95637 0.12 0.54776 0.52 0.69847 0.92 0.82121 1.32 0.90658 1.72 0.95728 0.13 0.55172 0.53 0.70194 0.93 0.82381 1.33 0.90824 1.73 0.95818 0.14 0.55567 0.54 0.70540 0.940.82639 1.34 0.90988 1.74 0.95907 0.15 0.55962 0.55 0.70884 0.95 0.82894 1.35 0.91149 1.75 0.95994 0.16 0.56356 0.56 0.71226 0.96 0.83147 1.36 0.91309 1.76 0.96080 0.17 0.56749 0.57 0.71566 0.97 0.83398 1.37 0.91466 1.77 0.96164 0.18 0.57142 0.58 0.71904 0.98 0.83646 1.38 0.91621 1.78 0.96246 0.19 0.57535 0.59 0.72240 0.99 0.83891 1.39 0.91774 1.79 0.96327 0.20 0.57926 0.60 0.72575 1.00 0.84134 1.40 0.91924 1.80 0.96407 0.21 0.58317 0.61 0.72907 1.01 0.84375 1.41 0.92073 1.81 0.96485 0.22 0.58706 0.62 0.73237 1.02 0.84614 1.42 0.92220 1.82 0.96562 0.23 0.59095 0.63 0.73565 1.03 0.84849 1.43 0.92364 1.83 0.96638 0.24 0.59483 0.64 0.73891 1.04 0.85083 1.44 0.92507 1.84 0.96712 0.25 0.59871 0.65 0.74215 1.05 0.85314 1.45 0.92647 1.85 0.96784 0.26 0.60257 0.66 0.74537 1.06 0.85543 1.46 0.92785 1.86 0.96856 0.27 0.60642 0.67 0.74857 1.07 0.85769 1.47 0.92922 1.87 0.96926 0.28 0.61026 0.68 0.75175 1.08 0.85993 1.48 0.93056 1.88 0.96995 0.29 0.61409 0.69 0.75490 1.09 0.86214 1.490.93189 1.89 0.97062 0.30 0.61791 0.70 0.75804 1.10 0.86433 1.50 0.93319 1.90 0.97128 0.31 0.62172 0.71 0.76115 1.11 0.86650 1.51 0.93448 1.91 0.97193 0.32 0.62552 0.72 0.76424 1.12 0.86864 1.52 0.93574 1.92 0.97257 0.33 0.62930 0.73 0.76730 1.13 0.87076 1.53 0.93699 1.93 0.97320 0.34 0.63307 0.74 0.77035 1.14 0.87286 1.54 0.93822 1.94 0.97381 0.35 0.63683 0.75 0.77337 1.15 0.87493 1.55 0.93943 1.95 0.97441 0.36 0.64058 0.76 0.77637 1.16 0.87698 1.56 0.94062 1.96 0.97500 0.37 0.64431 0.77 0.77935 1.17 0.87900 1.57 0.94179 1.97 0.97558 0.38 0.64803 0.78 0.78230 1.18 0.88100 1.58 0.94295 1.98 0.97615 0.39 0.65173 0.79 0.78524 1.19 0.88298 1.59 0.94408 1.99 0.97670 0.40 0.65542 0.80 0.78814 1.20 0.88493 1.60 0.94520 2.00 0.97725