Question

Conduct a test at the alphaequals0.10 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 123​, n 1 equals 248​, x 2 equals 141​, and n 2 equals 312. ​(a) Choose the correct null and alternative hypotheses below. A. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 greater than p 2 B. Upper H 0 : p 1 equals 0 versus Upper H 1 : p 1 not equals 0 C. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 not equals p 2 D. Upper H 0 : p 1 equals p 2 versus Upper H 1 : p 1 less than p 2 ​(b) Determine the test statistic. z0equals nothing ​(Round to two decimal places as​ needed.) ​(c) Determine the​ P-value. The​ P-value is nothing. ​(Round to three decimal places as​ needed.) What is the result of this hypothesis​ test? A. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 greater than p 2. B. Reject the null hypothesis because there is sufficient evidence to conclude that p 1 less than p 2. C. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 not equals p 2. D. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 less than p 2.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

b)

p1cap = X1/N1 = 123/248 = 0.496
p1cap = X2/N2 = 141/312 = 0.4519
pcap = (X1 + X2)/(N1 + N2) = (123+141)/(248+312) = 0.4714

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.496-0.4519)/sqrt(0.4714*(1-0.4714)*(1/248 + 1/312))
z = 1.04

c)

P-value Approach
P-value = 0.149

d)

As P-value >= 0.1, fail to reject null hypothesis.

A. Do not reject the null hypothesis because there is not sufficient evidence to conclude that p 1 greater than p 2