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

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

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)((1)/(n_1) +(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