Question

Conduct a test at the alphaequals0.05 level of significance by determining ​(a) the null and alternative​ hypotheses, ​(b) the test​ statistic, and​ (c) the​ P-value. Assume the samples were obtained independently from a large population using simple random sampling. Test whether p 1 greater than p 2. The sample data are x 1 equals 118​, n 1 equals 254​, x 2 equals 132​, and n 2 equals 306.

Answer 1

x1 = 118, n1=254, x2=132, n2=306, = 0.05

a) Ho: P1 P2

H1: P1 > P2

b)

calculate test statistics

Z= 0.786656

Z= 0.79

c) Calculate P-Value

P-Value = 1- P(Z<0.79)

Calculate P(Z<0.79) using normal Z table we get

P(Z<0.79) = 0.7852

P-Value = 1- 0.7852

P-value = 0.2148

Decision:

Since (P-Value = 0.2148) > ( = 0.05)

Hence Fail to reject Ho.

Conclusion:

Therefore there is not enough significant evidence to claim that P1>P2.