Question

Conduct a test at the

alpha

equals0.01

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 126

​,

n 1 equals 248

​,

x 2 equals 138

​,

and

n 2 equals 316

.

Answer 1

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

b)

p1cap = X1/N1 = 126/248 = 0.5081
p1cap = X2/N2 = 138/316 = 0.4367
pcap = (X1 + X2)/(N1 + N2) = (126+138)/(248+316) = 0.4681

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5081-0.4367)/sqrt(0.4681*(1-0.4681)*(1/248 + 1/316))
z = 1.69

c)

P-value Approach
P-value = 0.0455
As P-value >= 0.01, fail to reject null hypothesis.