Question

A random sample of 32 patients in a doctor’s office found that waiting times had a mean of 13 minutes with a standard deviation of 4.1 minutes. Based on this sample, a local doctor claims that the mean waiting time in their office is less than 15 minutes. At a 0.01 significance level, test the doctor's claim.

Choose the correct Null & Alternative Hypothesis and Conclusion with appropriate justification:

Select one:

H0:μ=13
H1:μ<15
Since the P-Value is ≈0.41 and that is greater than 0.01, Fail to Reject H0. There is not sufficient evidence the doctor may make the claim.

H0:μ=15
H1:μ<15
Since the P-Value is ≈0.005 and that is less than 0.01, Reject H0. There is sufficient evidence the doctor may make the claim.

H0:μ=15
H1:μ=13
Since the P-Value was ≈0.005 and that is less than 0.01, Fail to Reject H0. There is sufficient evidence the doctor may make the claim.

H0:μ=13
H1:μ<13
Since the P-Value is ≈0.005 and that is less than 0.01, Fail to Reject H0. There is sufficient evidence the doctor may make the claim.

H0:p=15
H1:p<13
Since the P-Value is ≈0.41 and that is greater than 0.01, Reject H0. There is sufficient evidence the doctor may make the claim.

H0:p=15
H1:p<15
Since the P-Value is ≈0.41 and that is greater than 0.01, Reject H0. There is not sufficient evidence the doctor may make the claim.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 15
Alternative Hypothesis, Ha: μ < 15

Rejection Region
This is left tailed test, for α = 0.01 and df = 31
Critical value of t is -2.453.
Hence reject H0 if t < -2.453

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (13 - 15)/(4.1/sqrt(32))
t = -2.759

P-value Approach
P-value = 0.005
As P-value < 0.01, reject the null hypothesis.

H0:μ=15
H1:μ<15
Since the P-Value is ≈0.005 and that is less than 0.01, Reject H0. There is sufficient evidence the doctor may make the claim.