Q4: Suppose in a clinical trial involving 91 liver cancer patients n1 = 34 were
ID: 3313993 • Letter: Q
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Q4: Suppose in a clinical trial involving 91 liver cancer patients n1 = 34 were treated with an experimental drug, and n2 = 57 were given the conventional treatment. The following contingency table reports the number of each group that experienced a recurrence within 6 months.
Q4: Suppose in a clinical trial involving 91 liver cancer patients n 34 were treated with an experimental drug, and n2 = 57 were given the conventional treatment. The following contingency table reports the number of each group that experienced a recurrence within 6 months. Experimental Treatment Standard Treatment Cancer recuras Cancer does not recur Total 31 3/ 12 45 57 15 76 91 Construct a level 0.95 confidence interval for the log odds ratio of recurrence between groups Experimental Treatment and Standard Treatment. Can you reject the null hypothesis Ho . OR-1 against Ha : OR 1 at significance level of = 0.05?Explanation / Answer
Given table data is as below MATRIX col1 col2 TOTALS row 1 3 12 15 row 2 31 45 76 TOTALS 34 57 N = 91 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 5.604 9.396 row 2 28.396 47.604 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 3 5.604 -2.604 6.781 1.21 12 9.396 2.604 6.781 0.722 31 28.396 2.604 6.781 0.239 45 47.604 -2.604 6.781 0.142 ^2 o = 2.313 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, = 0.05 from standard normal table, chi square value at right tailed, ^2 /2 =3.841 since our test is right tailed,reject Ho when ^2 o > 3.841 we use test statistic ^2 o = (Oi-Ei)^2/Ei from the table , ^2 o = 2.313 critical value the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.841 we got | ^2| =2.313 & | ^2 | =3.841 make decision hence value of | ^2 o | < | ^2 | and here we do not reject Ho ^2 p_value =0.128 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 2.313 critical value: 3.841 p-value:0.128 decision: do not reject HoRelated Questions
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