Hoping to reduce the waiting time, a doctor's office tried a new way of scheduling its appointments. Populations of waiting times are believed to be similar except in central tendency. However, waiting times may not be normally distributed, so a nonparametric test was chosen to compare the waiting times. The Wilcoxon/Mann-Whitney test results are shown below: $\text { Mann/Whitney Test }$

$\begin{array}{|c|c|c|}
\hline\text { n }&\text { sum of ranks }\
\hline 21 & 600.5& \text { Old Way}\
\hline 25 & 480.5& \text { New Way}\
\hline 46 & 1081& \text {
Total}\
\hline
\end{array}$

$493.50$ expected value
$45.31$ standard deviation
$2.35 \mathrm { z }$, corrected for ties
$.0094 \mathrm { p }$-value (one-tailed, upper) Which is the best conclusion?
A)The medians differ at ? = .01.
B)The means differ at ? = .01.
C)The samples differ at ? = .01.
D)There are no differences at ? = .01.

Question

Hoping to reduce the waiting time, a doctor's office tried a new way of scheduling its appointments. Populations of waiting times are believed to be similar except in central tendency. However, waiting times may not be normally distributed, so a nonparametric test was chosen to compare the waiting times. The Wilcoxon/Mann-Whitney test results are shown below: $\text { Mann/Whitney Test }$

$\begin{array}{|c|c|c|}
\hline\text { n }&\text { sum of ranks }\
\hline 21 & 600.5& \text { Old Way}\
\hline 25 & 480.5& \text { New Way}\
\hline 46 & 1081& \text { 
Total}\
\hline
\end{array}$

$493.50$ expected value
$45.31$ standard deviation
$2.35 \mathrm { z }$, corrected for ties
$.0094 \mathrm { p }$-value (one-tailed, upper) Which is the best conclusion?
A)The medians differ at ? = .01.
B)The means differ at ? = .01.
C)The samples differ at ? = .01.
D)There are no differences at ? = .01.

Quizplus · Accepted Answer

The null hypothesis is that there is no difference in waiting times between the old way and new way of scheduling appointments, while the alternative hypothesis is that the median waiting time for the new way is lower than the old way.

The p-value of 0.0094 is less than the significance level of 0.01, which means we reject the null hypothesis and conclude that there is evidence of a difference in waiting times between the old way and new way of scheduling appointments. Since the test is one-tailed, the conclusion is that the median waiting time for the new way is lower than the old way at α = .01. Option A is the best conclusion.

We cannot draw any conclusion about the means, as the test is nonparametric and does not assume normality. We also cannot say anything about the samples as a whole, only that there is evidence of a difference between the old and new ways of scheduling appointments.

Hoping to Reduce the Waiting Time, a Doctor's Office Tried Mann/Whitney Test \text { Mann/Whitney Test } Mann/Whitney Test

Hoping to Reduce the Waiting Time, a Doctor's Office Tried $\text { Mann/Whitney Test }$