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 117?, n 1 equals 243?, x 2 equals 138?, and n 2 equals 303.

Answer 1

(a)

H0: Null Hypothesis: p1 p2

HA: Alternative Hypothesis: p1 > p2

n1 = size of sample 1 = 243

1 = proportion of sample 1 = 117/243 = 0.4815

n2 = size of sample 2 = 303

2 = prportion of sample 2 = 138/303 = 0.4554

Q = 1 - P = 0.5330

Test statistic is:

Z = (1 - 2)/SE

= (0.4815 - 0.4554)/0.0430 = 0.6070

(c)

Table of Area Under Standard Normal Curve gives area = 0.2291

So,

p-value = 0.5 - 0.2291 = 0.2709

(d) Since p-value is greater than , Fail to reject H0.

Conclusion:

The data do not support the claim that p1 is greater than p2.