# Contingency Table & Probability

See attached template.

Using the Cereal worksheet (which we used in the Week 2 Lab for Linear Regression Analysis), the Calorie variable was recoded into "high calorie" and "low calorie" categories. We used 120 calories per serving as the break point (greater than or equal to 120 is "high calorie").

A contingency table was created inside the Cereal worksheet showing the breakdown of fiber and how it relates to calorie content. Use the contingency table to help answer the following probability questions. Write your answers inside the Week 4 Lab Template. You do not need to copy-and-paste anything from Excel.

Suppose one type of cereal is randomly selected.

1. What is the probability that the cereal would be high calorie? In other words, what is P(high calorie)?

2. What is the probability that the cereal would be high fiber? In other words, what is P(high fiber)?

3. What is the probability that a cereal would both high calorie and high fiber? In other words, what is P(high calorie and high fiber)?

4. What is the probability that a cereal would either high calorie or high fiber? In other words, what is P(high calorie or high fiber)?

5. What is the probability that a cereal would be high calorie, given that it is high fiber? In other words, what is P(high calorie, given high fiber)?

6. What is the probaility that a cereal would be high calorie, given that is is low fiber? In other words, what is P(high calorie, given low fiber)?

7. Regarding Questions 5 and 6, how might you interpret this information as a consumer?

8. Using the simple test of independence, decide if the events high calorie and high fiber are independent or dependent. Show your work.

9. Discuss how the Excel command "countif" was used in the table above. Why were the ranges (such as f2:f23) used as they were?

Place your answers inside the Week 4 Lab Template for submission. Be sure to follow the directions in the template.

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#### Solution Summary

The solution provides step by step method for the calculation of probabilities and conditional probabilities from the Cereal worksheet contingency table. Formula for the calculation and Interpretations of the results are also included.