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 318 seconds. For a sample of 45 patients, the mean time in which the medicine relieved pain was 323 seconds. Assume the population variance is known to be 324. Find the P-value of the test statistic. Round your answer to four decimal places. Is this a one tailed or two tailed test? Reject the HO > ?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 318
Alternative Hypothesis, Ha: μ > 318

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (323 - 318)/(18/sqrt(45))
z = 1.863

P-value Approach
P-value = 0.0312
As P-value < 0.05, reject the null hypothesis.