Question

Conduct a test at the alpha α equals = 0.01 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 p1>p2. The sample data are x1=128​, n1=245​, x2=144​, and n2=315.

​(a) Choose the correct null and alternative hypotheses below.

A.

H0: p1=p2 versus H1: p1<p2

B.

H0: p1=0 versus H1: p1≠0

C.

H0: p1=p2 versus H1: p1>p2

D.

H0: p1=p2 versus H1: p1≠p2

Answer 1

it is given that we have to test whether the proportion 1 is greater than proportion 2 or not.

So,it is simply a right tailed hypothesis for the proportion difference between proportion p1 and p2

Null hypothesis would be that there is no difference between two proportions

alternate hypothesis would be that the proportion1 is greater than proportion 2

Symbol form

option C

Using TI 84 calculator

press stat then tests then 2-PropZtest

enter the data

x1 = 128

n1 = 245

x2 = 144

n2 = 315

p1 > p2

press enter, we get

(b)z statistic = 1.534

(c) p value = 0.0625