In a comparative double-bind randomized study of single does fosfomycin trometam
ID: 3227533 • Letter: I
Question
In a comparative double-bind randomized study of single does fosfomycin trometamol with trimethoprim in the treatment of uncompleted urinary infections, 24 of 32 were cured with fosfomycin trometamol and 17 of 33 were cured with the reference drug trimethoprim Denote the eradication rates tor fosfomycin trometamol and the reference drug trimethoprim by p_1 and p_2 respectively. (a) Evaluate the test statistic Z = P_1 - P_2/Squareroot P(1 - P) (1/n_1 + 1/n_2) (b) Use the R function pnorm() and the value of the test statistic from (a) to find the p-value for the test H_0: P_1 = P_2 versus H_A: P_1 notequalto P_2- (c) Calculate a 94% two-sided confidence interval for the difference P_1 - P2 using the formula P_1 - P_2 plusminus z Squareroot P_1 (1 - P_1/n_1) + P_2 (1 - P_2/N_2) and the critical value z^* = 1.88087. The interval ranges from to .(d) Find the p-value for the test H_0: P_1 = P_2 H_A: P_1 notequalto P_2 using the R function prop.test(). (e) Are the eradication rates for the two drugs significantly different? Use the result of (d) and significance level alpha = 0.06 to answer this question. (f) Calculate a 94% two-sided confidence interval for the difference P_1 - P_2 using the R function prop.test(). The interval ranges from to .Explanation / Answer
a) The test-statistic is given by, Z = 1,96.
b) The p-value of the test is = 2 * P( Z > 1.96) where Z ~ N(0,1).
Hence p-value = 0.05.
c) 94% CI for p1 - p2 is given by = ( 0.0169, 0.4528).
d) The p-value = 2 * P (Z > 1.96) = 0.05.
e) Since p-value = 0.05 < 0.06. So the two drugs are significantly different at 6% level of significance.
f) The 94% CI for p1-p2 is given by = ( 0.0169, 0.4528)..