Question

Conduct a test at the alphaαequals=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

p 1 greater than p 2p1>p2. The sample data are x1=118​, n1=259​, x2=141​, and n2=313.

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

A.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 greater than p 2H1: p1>p2

B.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 not equals p 2H1: p1≠p2

C.

Upper H 0 : p 1 equals p 2H0: p1=p2

versus Upper H 1 : p 1 less than p 2H1: p1<p2

D.

Upper H 0 : p 1 equals 0H0: p1=0

versus Upper H 1 : p 1 not equals 0

B) Test the statistics

C) Find the P-value

Answer 1

Solution:

We are given that:

Level of significance =

x₁ = 118​, n₁=259​ then sample proportion =

x₂=141​, and n₂=313. then sample proportion =

We have to test whether p₁ > p₂.

Part A) Choose the correct null and alternative hypotheses below.

Since we have to test p₁ > p₂, option A) is correct.

A) H₀: p₁=p₂    Vs H₁: p₁>p₂

Part B) Test statistic:

where

Thus we get:

Part C) Find P-value:

P-value = P( Z > z test statistic value)

P-value = P( Z > 0.12)

P-value = 1 - P( Z < 0.12)

To P( Z < 0.12) , look in z table for z = 0.1 and 0.02 and find corresponding area.

from z table , we get:

P( Z < 0.12) =0.5478

Thus

P-value = 1 - P( Z < 0.12)

P-value = 1 - 0.5478

P-value = 0.4522