Question

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly less than 0.77. You use a significance level of α=0.002

      H0:p=0.77
      H1:p<0.77

You obtain a sample of size n=648 in which there are 486 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

less than (or equal to) α

greater than α

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is less than 0.77.

There is not sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is less than 0.77.

The sample data support the claim that the probability of a true negative on a test for a certain cancer is less than 0.77.

There is not sufficient sample evidence to support the claim that the probability of a true negative on a test for a certain cancer is less than 0.77.

Answer 1

= x / n = 486 / 648 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.75 - 0.77 / [(0.77 * 0.23) / 648]

= -1.21

P(z < -1.21) = 0.1131

P-value = 0.1131

= 0.002

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the probability of a true negative on a

test for a certain cancer is less than 0.77