The length of time that customers spent eating dinner was compared with and without music playing. The times, in minutes, were as follows. Without Music
$\begin{array}{c|c|c|c|c|c}
55 & 67 & 59 & 55 & 43 & 76 \
\hline 45 & 60 & 93 & 61 & 63 & 51
\end{array}$

With Music
$\begin{array}{l|l|l|l|l|l|l|l}
79 & 87 & 63 & 79 & 48 & 89 & 97 & 80 \
\hline 107 & 43 & 100 & 73 & 104 & 84 & 70 &
\end{array}$

a) Compute the P-value.
b) Can you conclude that the median times eating dinner differ with and without music? Use the $\alpha$ =0.01 level of significance.
A)a. 0.0086.
b. Yes, you can conclude that the median times are different.
B)a. 0.0086
b. No, you cannot conclude that the median times are different.
C) a. 0.0124.
b. Yes, you can conclude that the median times are different.
D)a. 0.0124
b. Yes, you can conclude that the median times are different.

Question

The length of time that customers spent eating dinner was compared with and without music playing. The times, in minutes, were as follows. Without Music
$\begin{array}{c|c|c|c|c|c}
55 & 67 & 59 & 55 & 43 & 76 \
\hline 45 & 60 & 93 & 61 & 63 & 51
\end{array}$

With Music
$\begin{array}{l|l|l|l|l|l|l|l}
79 & 87 & 63 & 79 & 48 & 89 & 97 & 80 \
\hline 107 & 43 & 100 & 73 & 104 & 84 & 70 &
\end{array}$

a) Compute the P-value.
b) Can you conclude that the median times eating dinner differ with and without music? Use the $\alpha$ =0.01 level of significance. 
A)a. 0.0086.
b. Yes, you can conclude that the median times are different.
B)a. 0.0086
b. No, you cannot conclude that the median times are different.
C) a. 0.0124.
b. Yes, you can conclude that the median times are different.
D)a. 0.0124
b. Yes, you can conclude that the median times are different.

Quizplus · Accepted Answer

a) To test for the difference in medians, we use the Wilcoxon Rank-Sum Test. The null hypothesis states that there is no difference in medians, and the alternative hypothesis states that there is a difference. Using a significance level of 0.01, we will reject the null hypothesis if the p-value is less than 0.01. Using software or a calculator, we find that the p-value is 0.0086.
b) Since the p-value is less than 0.01, we reject the null hypothesis and conclude that there is a significant difference in the median times eating dinner with and without music playing.

The Length of Time That Customers Spent Eating Dinner Was 556759554376456093616351\begin{array}{c|c|c|c|c|c}55 & 67 & 59 & 55 & 43 & 76 \\\hline 45 & 60 & 93 & 61 & 63 & 51\end{array}5545​6760​5993​5561​4363​7651​​

The Length of Time That Customers Spent Eating Dinner Was $\begin{array}{c|c|c|c|c|c}55 & 67 & 59 & 55 & 43 & 76 \\\hline 45 & 60 & 93 & 61 & 63 & 51\end{array}$