Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.10.1 level that the medicine relieves pain in more than 346346 seconds. For a sample of 1616patients, the average time in which the medicine relieved pain was 351351 seconds with a variance of 529529. Assume the population distribution is approximately normal.

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 three decimal places.

Step 3 of 5:

Specify if the test is one-tailed or two-tailed.

Step 4 of 5:

Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Step 5 of 5:

Make the decision to reject or fail to reject the null hypothesis.

Answer 1

1)

H0: <= 346

Ha: > 346

2)

Test statistics

t = - / S / sqrt(n)

= 351 - 346 / sqrt(529) / Sqrt( 16)

0.87

3)

This is one tailed test.

t critical value at 0.1 level with 15 df = 2.131

Decision rule = Reject H0 if t > 2.131

e)

Since test statistics falls in non-rejection region, we fail to reject the null hypothesis.