Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.05 level that the medicine relieves pain in more than 375 seconds. For a sample of 17 patients, the average time in which the medicine relieved pain was 383 seconds with a standard deviation of 20. Assume the population distribution is approximately normal.

Step 1 of 3:

State the null and alternative hypotheses.

Step 2 of 3:

Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 3 of 3:

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

Answer 1

Solution:
Null hypothesis H0: mean = 375 seconds
Alternate hypothesis Ha: mean > 375
Also given in the question
Sample mean = 383
Sample standard deviation = 20
No. of sample = 17
Population distribution is normal but no. of sample is less than 30 and population standard deviation is not known so we will use t test
test statistic can be calculated as
Test statistic = (Sample mean - population mean)/Sample standard deviation/Sqrt(n) = (383-375)/20/sqrt(17) = 1.65
here df = 17-1 = 16 and this is right tailed test
So p-value from t table is 0.059
Here we can see that p-value is greater than alpha value (0.059>0.05), so we are failed to reject the null hypothesis and we don't have significant evidence to support the claim i.e. the medicine relieves pain is not more than 375 seconds.