The student will evaluate data collected to determine if they fit either the uniform or exponential distributions.
Collect the data
Go to your local supermarket. Ask 30 people as they leave for the total amount on their grocery receipts. (Or, ask three cashiers for the last ten amounts. Be sure to include the express lane, if it is open.)
Note
You may need to combine two categories so that each cell has an expected value of at least five.
Record the values.
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Construct a histogram of the data. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
Calculate the following:
________
s = ________
s2 = ________
Uniform distribution
Test to see if grocery receipts follow the uniform distribution.
Using your lowest and highest values,
X ~
U (_______, _______)
Divide the distribution into fifths.
Calculate the following:
lowest value = _________
20
th percentile = _________
40
th percentile = _________
60
th percentile = _________
80
th percentile = _________
highest value = _________
For each fifth, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
Fifth
Observed
Expected
1
st
2
nd
3
rd
4
th
5
th
H
0 : ________
H
a : ________
What distribution should you use for a hypothesis test?
Why did you choose this distribution?
Calculate the test statistic.
Find the
p -value.
Sketch a graph of the situation. Label and scale the
x -axis. Shade the area corresponding to the
p -value.
State your decision.
State your conclusion in a complete sentence.
Exponential distribution
Test to see if grocery receipts follow the exponential distribution with decay parameter
.
Using
as the decay parameter,
X ~
Exp (_________).
Calculate the following:
lowest value = ________
first quartile = ________
37
th percentile = ________
median = ________
63
rd percentile = ________
3
rd quartile = ________
highest value = ________
For each cell, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
Cell
Observed
Expected
1
st
2
nd
3
rd
4
th
5
th
6
th
H
0 : ________
H
a : ________
What distribution should you use for a hypothesis test?
Why did you choose this distribution?
Calculate the test statistic.
Find the
p -value.
Sketch a graph of the situation. Label and scale the
x -axis. Shade the area corresponding to the
p -value.
State your decision.
State your conclusion in a complete sentence.
Discussion questions
Did your data fit either distribution? If so, which?
In general, do you think it’s likely that data could fit more than one distribution? In complete sentences, explain why or why not.