Question

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for more than 363 minutes. For a sample of 45 patients, the mean time the drug stayed in the system was 367 minutes. Assume the population variance is known to be 484.

Step 1 of 5 : State the null and alternative hypotheses.

Step 2 of 5 :  Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5 : Specify if it is one tailed or two tailed

Step 4 of 5 :  Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 5 : Make the decision to reject or fail to reject the null hypothesis.

Answer 1

This is the right(one) tailed test .

The null and alternative hypothesis is

H₀ : = 363

H_a : > 363

Test statistic = z

= ( - ) /    / n

= (367 - 363) / 22 / 45

Test statistic = 1.22

P-value = 0.1113

P-value >

Fail to reject the null hypothesis .