Question

14 pores The Stanford Un e sty Hekrt Transp ant Study was to ducted to deter ne whet er e pe me ta heart tra spart program ncreased ega tach pate e emer ng the progam as des aled an aEce heart t splant canádate, meri g that he was grave il and would most ike tom s new hert Pst entl the trem e e group Qot ฮ 1 ข 5p ข t ข d those the contro poup dd mot the 34 patents n the contro Voup. 4 were 3 ve ข↑ the end o the tuty the 89 psten, t e mest ent group 24 were 3 ve The oor gen y t80le beon"um martes these esut benefit Trestment 24 45 ota 28 7 103 Round al calculsted answers to fout decimal places . Whar propon ofcatenta in he treatmant group aurvid 2. What proportion ofpatients in the control group surviwed 1. Wha in the dipropartions ad one approaen tor investgang whather or not the ข"tram s enectva s to use randomization technique Complete the staemens for the hull and ateative hypothesis Ho: The variablas Surival and Tretnt HA The varabies Survival and Treatmant? T paragraph balow descrbes sat up for ach appoach, f wa ware so de .We wrte treatment o and anotner gro.p ofsz may times to builddistrèution centered at should be rejected in favor of the stermative independant Th๑ diftaranea in survival ratas n the tsaarmant and conceal group 7 due to ehanoa. wihout uzing atcal aoar Fill in the lanika wth a number or phraze whichaver la approprata cards representing patients who were in the treatment group. and control cands representing patients in the contral group Then we shuffie fhese cards and spit them into two groups one group of size representing patients who survived. prese trg pane ts no ded. We ca custe the d ere oe beween the propo non a patents n the t ement roup w o su ved and te propo ton of patients n the comrol จ○up who survived to pet P P A ㎖ ธ d ecord tes value Yve repeat the Lastly we calcu ate the taction of simulations wherthesimuled deences in praportion? If this frction is low, we conclude thet it is unikey to have obeerved such an outcome by chance and that the ull hypothesis Whan do the simulatons shown blow suggst aboat the aevas thetransplant program7 -0.25 -0.15 -0.05 0.05 0.15 0.25 Simulated differences in proportions A Snca hare a B. Snce are a vary faw simulated ditarencea tha: are larger an 23, the tranaplant program apcear to be sffective vary faww simulated ditarencea tha: are larper an 23 the tranaplant program doas not appear to be fectiva. 0 snea fro61 ofthie iimulased dFerencas are iesk than 0 23, tha laselant program does not appear to be eneesv๑ O D. Since the simulsted diferences appear to be centered around 0. the transçlent program appesrs to be effective

Answer 1

1)

The proportion of patients in the treatment group that survived is

P, 24/69-03478

2)

The proportion of patients in the control group that survived is

P, 4/34-0.1 176

3)

The Difference in the proportions is

Pi-P, = 0.3478-0.1176 0.2302

4)

H_0: The variables Survival and Treatment are independent. The difference in survival rates in the treatment and control group is purely due to chance.

H_A: The variables Survival and Treatment are not independent. The difference in survival rates in the treatment and control group is not due to chance.

5)

We write treatment on 69 cards representing ..... and control on 34 cards .... one group of size 28 representing patients who survived. and another on size 75 representing patients who died. We calculate .. in proportion are larger than 0.23.

6)

Since there are very few simulated differences larger than 0.23, the transplant program appears to be effective.

The low number of simulations over 0.23 tell us that there is a low chance of getting higher than 0.23 difference in the proportions. So we can say that the treatment is effective.