Question

The following data represent the time, in minutes, that a patient has to wait during 12 visits to a doctor’s office before being seen by the doctor:

17 15 20 20 32 28 12 26 25 25 35 24

Use a test at the 0.05 level of significance to test the doctor’s claim that the median waiting time for her patients is not more than 20 minutes.

Can you use the Wilcoxon Rank-Sum Test or a t-test? If yes, perform the test. If no, then explain why not.

Answer 1

The data represent the time, in minutes, that a patient has to wait during 12 visits to a doctor's office before being seen by the doctor. Test the doctor's claim that the median waiting time for her patients is not more than 20 minutes before being admitted to the examination room.

The data comprise a Single Sample. The response is a score reported as an integer.

The appropriate method is the sign test for the median.

Analytical Method Selected: sign test

Hypotheses

Null: The population median is 20.

Alternate: The population median is greater than 20.

p-value = 0.1714

Decision: Fail to reject the null hypothesis.

Conclusion: Based on the sample data, the population median is not greater than 20 minutes.

The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test (also known as "t-test for matched pairs" or "t-test for dependent samples") when the population cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution.

So, we can't use Wilcoxon Rank Sum Test. And for t-test the assumption of normally distributed data is not full filled so we can't use t-test.