Chapter 11 Chi Square Goodness of Fit Lab

Chapter 11 Lab 1: Chi –Square Goodness of Fit Class Time: ______

Names: ______

______

ANSWERS MAY BE TYPED OR HAND-WRITTEN NEATLY BELOW.

Student Learning Outcome: The student will evaluate whether student preferences for their favorite type of snack are uniformly distributed across four snack groups.

I. Observed Data and Expected Distribution. Observed Class Data from several past statistic classes: Sweets (candy Chips & Fruits & Type of Snack Ice Cream TOTAL & baked goods) Pretzels Vegetables Observed Frequency

1. Fill in the expected distribution of snack preferences, assuming they are uniformly distributed. Sweets (candy Chips & Fruits & Type of Snack Ice Cream TOTAL & baked goods) Pretzels Vegetables Observed Frequency

2. Looking at the above charts does it appear to you that students’ snack preferences are uniformly distributed? Use COMPLETE SENTENCES to explain why or why not by properly comparing various numbers and/or percentages. Be clear and specific.

II. Conduct a goodness of fit hypothesis test to determine if student preferences for their favorite type of snack are uniformly distributed across four snack groups. 1. Ho: ______

______

2. HA: ______

______3. Distribution to use for the hypothesis test:______4. The sequence of calculator commands to find the test statistic are:

Write the symbol and the value of the test statistic. Symbol: ______Value: ______

5. Write the calculator command, including parameters to find the p-value (to 4 decimal places):

Calculator command: ______p-value : ______6. Draw a graph of the situation. NEATLY label and shade the graph, identifying areas and values for both  and the p-value. Label the mean of the distribution.

7. What is your decision for this hypothesis test? You must justify your decision clearly for credit.

Decision: Justification:

8. State your conclusion for this hypothesis test, in complete sentences, in the context of the situation of this lab. Chapter 11 Lab 2: Test for Independence Student Learning Outcome: The student will evaluate whether student preferences for favorite type of snack are independent of gender.

I. Observed Data and Expected Distribution: Observed Class Data based on several past statistic classes: Type of Snack Sweets (candy Ice Chips & Fruits & OBSERVED TOTAL & baked goods) Cream Pretzels Vegetables Frequency MALE FEMALE TOTAL 2. Looking at the above chart does it appear to you that a person’s favorite type of snack food DEPENDS on gender? Use COMPLETE SENTENCES to explain why or why not by properly comparing various numbers and/or percentages. Be clear and specific.

II. Conduct a hypothesis test to determine if student snack preferences are independent of gender.

1. Ho: ______

2. HA:______

3. Distribution to use for the hypothesis test:______

4. Write the symbol and calculate the value of the test statistic: Symbol: ______Value: ______

The calculator commands to find the test statistic are: Stat  Test  ______

5. Find the p-value (to four decimal places): ______6. Draw a graph of the situation. NEATLY label and shade the graph, identifying areas and values for both  and the p-value. Label the mean of the distribution.

7. What is your decision for this hypothesis test? You must justify your decision clearly for credit. Decision: Justification: 8. State your conclusion for this hypothesis test, in complete sentences, in the context of the situation of this lab.

9. a. Fill in the expected distribution (estimates to 4 decimal places) of snack preferences that would be obtained if snack preferences were independent of gender. Type of Snack Sweets (candy Chips & Fruits & Ice Cream TOTAL EXPECTED DATA & baked goods) Pretzels Vegetables MALE FEMALE TOTAL b. Now, show the specific calculations, using the appropriate numbers, how the expected value for female students who prefer ice cream would be calculated from your original data.

Calculations: