Question

The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.1 level that the drug stays in the system for more than 364 minutes. For a sample of 82 patients, the mean time the drug stayed in the system was 368 minutes. Assume the population standard deviation is 21.

(a) Is it a left tailed or a right tailed or a two tailed test?
(b) Compute the test statistic.
(c) Make the decision to reject or fail to reject the null hypothesis.

Answer 1

This is a right-tailed test with a test statistic of 0.9042. The null hypothesis is not rejected.

Step-by-step explanation:

(a) This is a right-tailed test because the alternative hypothesis states that the drug stays in the system for more than 364 minutes.

(b) The test statistic can be calculated using the formula:
t = (sample mean - null hypothesis mean) / (population standard deviation / sqrt(sample size))
Plugging in the values, we get t = (368 - 364) / (21 / sqrt(82))

= 0.9042.

(c) To make the decision, we compare the test statistic with the critical value from the t-distribution table. Since the test statistic is less than the critical value, we fail to reject the null hypothesis.

There is not enough evidence to conclude that the drug stays in the system for more than 364 minutes at the 0.1 level of significance.