Question

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

Upper H 0H0​:

pequals=0.40.4

versus

Upper H 1H1​:

pgreater than>0.40.4

nequals=100100​;

xequals=5050​;

alphaαequals=0.05

1) Calculate the test statistic, Z0

2) Identify the P Value

3)Choose the correct result:

- Do not reject the null hypothesis; b/c the p value is less than α

-Do not reject the null hypothesis; b/c the p value is greater than α

- Reject the null hypothesis; b/c the p value is less than α

- Reject the null hypothesis; b/c the p value is greater than α

Answer 1

1) The following null and alternative hypotheses need to be tested:

This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used.

The z-statistic is computed as follows:

Since it is observed that z=2.041>zc​=1.64, it is then concluded that the null hypothesis is rejected.

2) The p-value is p=0.0206, and since p=0.0206<0.05, it is concluded that the null hypothesis is rejected.

3) It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than p0​, at the α=0.05 significance level.