A consumer advocate decided to investigate the average wait time for a table for one at two local restaurants.Eighteen customers were sent to each restaurant at the same randomly selected times and the times they waited for a table were recorded in minutes.The following sample data was obtained. $$\begin{array} { r r | l r }
&\text { Restaurant } \mathrm { A } & \text { Restaurant } \mathrm { B } \
\hline 10 & 15 & 12 & 17 \
7 & 9 & 5 & 12 \
20 & 5 & 8 & 2 \
15 & 5 & 10 & 25 \
7 & 0 & 6 & 35 \
10 & 12 & 10 & 14 \
19 & 6 & 9 & 22 \
0 & 5 & 20 & 18 \
22 & 18 & 5 & 13
\end{array}$$ Find a 95% confidence interval for the difference, $\mu _ { \mathrm { A } }$ - $\mu \mathrm { B }$ ,between the mean wait time at Restaurant A and the mean wait time at Restaurant B.
A)(-8.3,1.86)
B)(-1.86,8.3)
C)(-8.3,-1.86)
D)(-13.5,-10.28)
E)(10.28,13.5)

Question

A consumer advocate decided to investigate the average wait time for a table for one at two local restaurants.Eighteen customers were sent to each restaurant at the same randomly selected times and the times they waited for a table were recorded in minutes.The following sample data was obtained. $$\begin{array} { r r | l r } 
&\text { Restaurant } \mathrm { A } & \text { Restaurant } \mathrm { B } \
\hline 10 & 15 & 12 & 17 \
7 & 9 & 5 & 12 \
20 & 5 & 8 & 2 \
15 & 5 & 10 & 25 \
7 & 0 & 6 & 35 \
10 & 12 & 10 & 14 \
19 & 6 & 9 & 22 \
0 & 5 & 20 & 18 \
22 & 18 & 5 & 13
\end{array}$$ Find a 95% confidence interval for the difference, $\mu _ { \mathrm { A } }$ - $\mu \mathrm { B }$ ,between the mean wait time at Restaurant A and the mean wait time at Restaurant B.
A)(-8.3,1.86)
B)(-1.86,8.3)
C)(-8.3,-1.86)
D)(-13.5,-10.28)
E)(10.28,13.5)

Quizplus · Accepted Answer

The correct confidence interval for the difference between the mean wait times at Restaurant A and Restaurant B is (-8.3, 1.86). This interval suggests that the true difference in mean wait times could range from Restaurant A having an average wait time that is 8.3 minutes less than Restaurant B, to Restaurant A having an average wait time that is 1.86 minutes more than Restaurant B, with 95% confidence.

A Consumer Advocate Decided to Investigate the Average Wait Time