Question

Consider the following hypotheses.

Upper H0​: p≤0.25

Upper H1​: p>0.25

Given that p=0.3​, n=110​, and α=0.05 answer the following questions.

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

Upper H0​: p≤0.25

Upper H1​: p>0.25

=0.3

P0 = 0.25

1 - P0 = 0.75

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.3-0.25 / [(0.25*0.75) / 110]

= 1.21

P(z >1.21 ) = 1 - P(z <1.21 ) = 1-0.8869=0.1131

P-value = 0.1131

= 0.05

P-value >

fail to Reject the null hypothesis .