Question

in a rwandom sample of 54 patients undergoing a standar4d surgical procedure4, 10 required pain medication foer postoperative pain. in a random sample of 80 patients undergoinmg a new procedure, 19 required pain medication. test the claim that fewer patients require pain medication

Answer 1

Answer)

Null hypothesis Ho : p1 = p2

Alternate hypothesis Ha : p1 < p2

N1= 54, P1 = 10/54

N2 = 80, P2 = 19/80

First we need to check the conditions of normality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are greater than equal to 5 or not

N1*p1 = 10

N1*(1-p1) = 44

N2*p2 = 19

N2*(1-p2) = 61

All the conditions are met so we can use standard normal z table to conduct the test

Test statistics z = (P1-P2)/standard error

Standard error = √{p*(1-p)}*√{(1/n1)+(1/n2)}

P = pooled proportion = [(p1*n1)+(p2*n2)]/[n1+n2]

After substitution

Test statistics z = -0.72

From z table, P(Z<-0.72) = 0.2358

So, P-Value = 0.2358

As the obtained P-Value is greater than the given significance

We fail to reject the null hypothesis Ho.

We do not have enough evidence to conclude that p1 < p2