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Statistics

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

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

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

Stats Lab

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.
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