Question

Conduct a test at the a= 0.05 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 p1 >p2. The sample data are x1=121, n1=258, x2=144, n2=317

B. Determine the Test Statistic. z0= ? (Round to two decimal places).

C. Determine the P-Value = ? (Round to Three Decimal Places).

Please label answers B & C when responding.

Answer 1

B) = 121/258 = 0.47

   = 144/317 = 0.45

The pooled sample proportion (P) = ( * n1 + * n2)/(n1 + n2) = (0.47 * 258 + 0.45 * 317)/(258 + 317) = 0.46

The test statistic z = ()/sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.47 - 0.45)/sqrt(0.46(1 - 0.46)(1/258 + 1/317))

= 0.48

c) P-value = P(Z > 0.48)

= 1 - P(Z < 0.48)

= 1 - 0.6844

= 0.3156