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

Lab 1: Chi-Square Goodness-of-Fit

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.

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. $\overline{x}$ = ________
   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. 20^th percentile = _________
   3. 40^th percentile = _________
   4. 60^th percentile = _________
   5. 80^th 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. H_a: ________
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 $\frac{1}{\overline{x}}$.

1. Using $\frac{1}{\overline{x}}$ as the decay parameter, X ~ Exp(_________).
2. Calculate the following:
   1. lowest value = ________
   2. first quartile = ________
   3. 37^th percentile = ________
   4. median = ________
   5. 63^rd percentile = ________
   6. 3^rd 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. H_a: ________
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.