Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. H0​: p=0.4 versus H1​: p>0.4 n=250​; x=110​, α=0.05

Is np01−p0≥​10? (no or yes???)

​P-value=() ​(Round to three decimal places as​ needed.)

(reject or do not reject???) the null hypothesis, because the​ P-value is( greater or less????) than α.

Answer 1

We are testing here whether the population proportion is more than 0.4, therefore this is a one tailed test here.

The sample proportion here is computed as:
p = x/n = 110/250 = 0.44

The test statistic here is computed as:

As this is a one tailed test, the p-value here is obtained from the standard normal tables as:
p = P(Z > 1.29) = 0.0985

Therefore 0.099 is the required p-value here.

As the p-value here is 0.099 > 0.05 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the population proportion is more than 0.4.