Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

Upper H 0​: p = 0.3 versus Upper H 1​: p > 0.3 n = 200​; x = 80​; a = 0.05

Answer 1

Requirement test:

Since p=0.3 so, q=1-p=0.7 and sample size 200 so

n*p=0.3*200= 60>5

n*q=0.7*200=210>5 so, we can assume it as normal distribution and use Z statistic for hypothesis testing.

Given that n = 200​; x = 80 so, sample proportion will be:

The Hypotheses are:

H_o​: p = 0.3

H₁​: p > 0.3

Based on the hypothesis we will use a one-tail test.

Rejection region:

At 0.05 level of significance reject Ho if Z>Z_0.05 =1.645 ( Computed using Z table shown below)

Test statistic:

P-value:

The P-value is computed using Z table shown below at Z score calculated above as:

P-value=0.001

Conclusion:

Since P-value<<0.05 hence we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Z table: