Question

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly different from 0.16. Thus you are performing a two-tailed test. Your sample data produce the test statistic z=−3.214. Find the p-value accurate to 4 decimal places.

p-value =

Answer 1

Given:

Hypothesis:

Ho: p = 0.16

Ha: p 0.16 (Two tailed test)

Test statistic (Z) = -3.214

Here, we assume that, = 0.05

P-value: 0.0013 ..................Using software

Conclusion:

P-value < , i.e. 0.0013 < 0.05, That is Reject Ho at 5% level of significance.

There is sufficient evidence to support the claim that the probability of a true negative on a test for a certain cancer is different from 0.16.

Answer 2

Given:

Hypothesis:

Ho: p = 0.16

Ha: p 0.16 (Two tailed test)

Test statistic (Z) = -3.214

Here, we assume that, = 0.05

P-value: 0.0013 ..................Using software

Conclusion:

P-value < , i.e. 0.0013 < 0.05, That is Reject Ho at 5% level of significance.

There is sufficient evidence to support the claim that the probability of a true negative on a test for a certain cancer is different from 0.16.