Skip to ContentGo to accessibility page
Statistics

# 11.7Lab 1: Chi-Square Goodness-of-Fit

Statistics11.7 Lab 1: Chi-Square Goodness-of-Fit
Stats Lab 11.1

#### 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 DataGo 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.
1. Record the values.
 __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________
Table 11.23
2. Construct a histogram of the data. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
Figure 11.9
3. Calculate the following:
1. $x ¯ x ¯$ = ________
2. s = ________
3. s2 = ________

Uniform Distribution Test to see if grocery receipts follow the uniform distribution.

1. Using your lowest and highest values, X ~ U (_______, _______).
2. Divide the distribution into fifths.
3. Calculate the following:
1. lowest value = _________
2. 20th percentile = _________
3. 40th percentile = _________
4. 60th percentile = _________
5. 80th percentile = _________
6. highest value = _________
4. 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
Table 11.24
5. H0: ________
6. Ha: ________
7. What distribution should you use for a hypothesis test?
8. Why did you choose this distribution?
9. Calculate the test statistic.
10. Find the p-value.
11. Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the p-value.
Figure 11.10
12. State your decision.
13. State your conclusion in a complete sentence.

Exponential Distribution Test to see if grocery receipts follow the exponential distribution with decay parameter $1 x¯ 1 x$.

1. Using $1 x ¯ 1 x ¯$ as the decay parameter, X ~ Exp(_________).
2. Calculate the following:
1. lowest value = ________
2. first quartile = ________
3. 37th percentile = ________
4. median = ________
5. 63rd percentile = ________
6. 3rd quartile = ________
7. highest value = ________
3. 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
Table 11.25
4. H0: ________
5. Ha: ________
6. What distribution should you use for a hypothesis test?
7. Why did you choose this distribution?
8. Calculate the test statistic.
9. Find the p-value.
10. Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the p-value.
Figure 11.11
11. State your decision.
12. State your conclusion in a complete sentence.
Discussion Questions
1. Did your data fit either distribution? If so, which?
2. In general, do you think it’s likely that data could fit more than one distribution? In complete sentences, explain why or why not.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Attribution information
• If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/statistics/pages/1-introduction
• If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/statistics/pages/1-introduction
Citation information

© Jan 26, 2021 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.