Question

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.1 level (α=0.1) that the medicine relieves pain in less than 420 seconds. For a sample of 51 patients, the mean time in which the medicine relieved pain was 400 seconds. Assume the population standard deviation is known to be 75.

What is the conclusion of testing at the 0.1 level of significance (α=0.1)?

Reject the Null Hypothesis. Based on the sample data, there is sufficient evidence to conclude that the medicine relieves pain in less than 420 seconds.

None of the above

Reject the Null Hypothesis. Based on the sample data, there is insufficient evidence to conclude that the medicine relieves pain in less than 420 seconds.

Fail to Reject the Null Hypothesis. Based on the sample data, there is insufficient evidence to conclude that the medicine relieves pain in more than 420 seconds.

Reject the Null Hypothesis. Based on the sample data, there is sufficient evidence to conclude that the medicine relieves pain in more than 420 seconds.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 420
Alternative Hypothesis, Ha: μ < 420

Rejection Region
This is left tailed test, for α = 0.1
Critical value of z is -1.28.
Hence reject H0 if z < -1.28

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (400 - 420)/(75/sqrt(51))
z = -1.9

P-value Approach
P-value = 0.0287
As P-value < 0.1, reject the null hypothesis.

Reject the Null Hypothesis. Based on the sample data, there is sufficient evidence to conclude that the medicine relieves pain in less than 420 seconds.