Question

Conduct a test at the a=0.05 level of significance by determining (a) null and alternative hypothesis, (b) the test statistic, (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=117 n1=249 x2=141 n2=312

Answer 1

Answer:

Since p > alpha, we accept H0, there is no evidence to prove that p1 is greater than p2

Step-by-step explanation:

Set up hypotheses as

$H_0: p1 = p2\\H_a: p1>p2$

(Right tailed t test)

Alpha = 0.05

Sample               I                II                Total

X                        117             141              248

N                        249           312            561

p                        0.4700     0.4519        0.4420

p difference = 0.0181    

Std dev = $\sqrt{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2} )}$

=0.0427

z statistic = 0.424

p value = 0.33724

Since p > alpha, we accept H0, there is no evidence to prove that p1 is greater than p2