n a comparative doubleblind randomized study of single dose

n a comparative double-blind randomized study of single dose fosfomycin trometamol with trimethoprim in the treatment of uncomplicated urinary infections, 25 of 33 were cured with fosfomycin trometamol and 13 of 25 were cured with the reference drug trimethoprim.

Denote the eradication rates for fosfomycin trometamol and the reference drug trimethoprim by p1 and p2 respectively.

(a) Evaluate the test statistic

Z=p 1p 2p (1p )(1n1+1n2).

________

(b) Use the R function pnorm() and the value of the test statistic from (a) to find the p-value for the test H0:p1=p2 versus HA:p1p2. _______

(c) Calculate a 91% two-sided confidence interval for the difference p1p2 using the formula

p 1p 2±zp 1(1p 1)n1+p 2(1p 2)n2

and the critical value z=1.6954. The interval ranges from _______ to ________ .

(d) Find the p-value for the test H0:p1=p2 versus HA:p1p2 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 =0.09 to answer this question. _________.

(f) Calculate a 91% two-sided confidence interval for the difference p1p2 using the R function prop.test(). The interval ranges from _____ to _____.

Solution