Statistics · The Chi-Square Distribution
Lab 1: Chi-Square Goodness-of-Fit
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Lab 1: Chi-Square Goodness-of-Fit
Student Learning Outcome 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 3 cashiers for the last 10 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.
Construct a histogram of the data. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes. View original figure (external; image not reproduced in this text edition)
Original figure description: Blank graph with relative frequency on vertical
Calculate the following:
x
¯
= ________s = ________s 2 = ________
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 = _________
20th percentile = _________
40th percentile = _________
60th percentile = _________
80th 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.
H0 : ________Ha : ________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. View original figure (external; image not reproduced in this text edition)
Original figure description: Blank graph with vertical and horizontal axes.
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
1
x
.
Using
1
x
¯
as the decay parameter, X ~ Exp (_________).
Calculate the following:
lowest value = ________
first quartile = ________
37th percentile = ________
median = ________
63rd percentile = ________
3rd 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.
H0 : ________Ha : ________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. View original figure (external; image not reproduced in this text edition)
Original figure description: Blank graph with vertical and horizontal axes.
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.
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