Question

Conduct the following test at the a = 0.05 level of significance by determining (a) the null and alternative hypotheses (b) the test statistic (c) the critical value (d) the P-value. Assume that the samples were obtained independently using simple random sampling. Test whether p1 does not equal p2. Sample data are x1 = 30, n1=254, x2 =38 and n2 =302.

Answer 1

(a) The null and alternative hypothesis

(b) Test statistic

where

n1=254, n2=302

= 0.1223

Q=1-P=0.8777

Therefore ,

= -0.28

Thus, test statistic is

z=-0.28

(c) At a=0.05 , two tailed critical value of z is

zc = 1.96

Since calculated value of z , IzI < 1.96 , critical value

We fail to reject H0

There is not sufficient evidence  to conclude that p1 is not equal to p2

(d) P value = 0.7795

Since P value >0.05

We

fail to reject H0

There is not sufficient evidence  to conclude that p1 is not equal to p2