Question

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.05 level that the drug stays in the system for more than 316 minutes. For a sample of 34 patients, the mean time the drug stayed in the system was 319 minutes. Assume the population variance is known to be 441.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test.

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Hypothesis: Vs  

Since , the population standard deviation is known.

Therefore , use normal distribution.

Step 2 of 6 : The value of the test statistic is ,

Step 2 of 6 : The test is one-tailed test.

Step 2 of 6 : The p-value is ,

p-value =

; From standard normal distribution table

Step 2 of 6 : The level of significance is

Step 2 of 6 : Decision : Here , p-value = 0.2033 >

Therefore , fail to reject the null hypothesis