The Chi-Square Distribution: Lab I 1.5 2008/06/19 13:49:12 GMT-5 2008/08/15 13:30:00.160 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics This module provides a lab on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean. Class Time: Names:

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.) Record the values. __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ Construct a histogram of the data. Make 5 - 6 intervals. Sketch the graph using a ruler and pencil. Scale the axes.

Calculate the following: ax¯= size 12{ {overline {x}} } {} bs= size 12{s} {} cs2= size 12{s rSup { size 8{2} } } {}

Uniform Distribution Test to see if grocery receipts follow the uniform distribution. Using your lowest and highest values, X ~ U_______,_______ size 12{X "~" U left ("_______, _______" right )} {} Divide the distribution above into fifths. Calculate the following: aLowest value = b20th percentile = c40th percentile = d60th percentile = e80th percentile = fHighest 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 1st 2nd 3rd 4th 5th Ho size 12{H rSub { size 8{o} } } {}: Ha size 12{H rSub { size 8{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 1 x . Using 1x¯ size 12{ { {1} over { {overline {x}} } } } {} as the decay parameter, X ~ Exp_______ size 12{X "~" ital "Exp" left ("_______" right )} {}. Calculate the following: aLowest value = bFirst quartile = c37th percentile = dMedian = e63rd percentile = f3rd quartile = gHighest 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 1st 2nd 3rd 4th 5th 6th Ho size 12{H rSub { size 8{o} } } {} Ha size 12{H rSub { size 8{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.