Question

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 397 minutes. For a sample of 62 patients, the mean time the drug stayed in the system was 402 minutes. Assume the population standard deviation is 18. Find the P-value of the test statistic. Round your answer to four decimal places.

Answer 1

Solution :

= 397

=402

= 18

n = 62

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 397

H_a : > 397

Test statistic = z

= ( - ) / / n

= (402 -397) / 18 / 62

= 2.187

Test statistic = z = 2.19

P(z >2.19 ) = 1 - P(z < 2.19 ) = 1 - 0.9857

P-value =0.0143

= 0.01

P-value ≥

0.0143 ≥ 0.01

Do not reject the null hypothesis .

Therefore, there is not enough evidence to claim that the population mean μ is greater than 397