
Exponential Distribution
3. Determine if the Exponential Distribution can be used to model the data given below. The data are the times between consecutive truck arrivals at a landfill, starting at an arbitrary time. Use the Chi Squared Goodness of Fit Test. As you work through the parts of the problem, create the appropriate “Chi Squared Goodness of Fit Test” Table. Document the calculations used to make the table (see my student resources page for information on documenting work in tables).
Truck Minutes
1 1.0
2 3.8
3 6.1
4 0.8
5 0.4
6 4.4
7 12.8
8 0.8
9 0.5
10 0.8
11 6.5
12 2.8
13 0.5
14 7.6
15 2.0
16 2.3
17 0.5
18 3.5
19 0.6
20 2.2
(First truck arrived 1 minute after timing started, second truck arrived 3.8 minutes after first truck, etc.)
a. Determine the n values for the following ranges (03, 36, 69, 912 & >12 minutes). [I got 1 for the last range.]
b. What is the average truck arrival rate (trucks/min)? [Hint: it took how long for 20 trucks to arrive?]
c. Determine the theoretical probabilities associated with the same ranges (use Exponential Dist). [I got 0.02 for the last range.]
d. Determine the e values for the same ranges. [I got 0.36 for the last range.]
e. Determine the portion of the C Test Statistic associated with each of same ranges. [I got 1.11 for the last range.]
f. Determine the C Test Statistic.
g. Determine the appropriate degrees of freedom.
h. If a type 1 error of 0.05 is used, what is the critical value (CV)?
i. Compare C to CV. What conclusion should we draw about using the Exponential?