1) A restaurant has three separate dining areas: the patio, the alcove, and the
ID: 3361567 • Letter: 1
Question
1) A restaurant has three separate dining areas: the patio, the alcove, and the flli all. At question is whether the median dollar amount per customer is the same or different between these three restaurant locations. To test this, the manager has randomly selected samples from each location. These data are shown as follows: Patio Alcove Main Hall $22.45 $20.20 $35.70 $19.50 $%18.50 $17.90 $30.00 $%19.60 $25.50 $18.25 $19.50 $22.50 $32.00 $14.50 $%14.50 $30.20 $17.80 $25.00 $40.00 $34.50 $28.70 $15.75 $36.50 $21.30 a. If the manager is unwilling to make the assumption that the bill amounts are normally distributed at all three locations, explain what statistical technique would you suggest to test whether the median bill amounts are the same or different? (5 marks) b. State the appropriate null and alternative hypotheses. (5 marks) c. Using an alpha level equal to.05(5.99), test the null hypothesis and state your conclusion. (10 marks) (20 marks)Explanation / Answer
Result:
a). nonparametric median test can be used.
b).
MINITAB used.
Null hypothesis
H: The population medians are all equal
Alternative hypothesis
H: The population medians are not all equal
Mood's Median Test: bill amount versus grp
Descriptive Statistics
grp
Median
N <= Overall Median
N > Overall Median
Q3 – Q1
95% Median CI
alcove
19.850
6
2
4.2875
(17.5876, 22.9827)
main hall
26.850
3
5
15.1000
(18.3230, 34.8540)
patio
23.975
3
5
16.0250
(17.6812, 35.7515)
Overall
21.875
Test
DF
Chi-Square
P-Value
2
3.00
0.223
Calculated chi square value 3.0 is < critical value 5.99.
Ho is not rejected.
We conclude that the median bill amounts are same for the three locations.
Null hypothesis
H: The population medians are all equal
Alternative hypothesis
H: The population medians are not all equal
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