# 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.

Contingency Table and Probability

Many people think that job satisfaction in the workplace is directly related to the annual income. To check the validity of this assumption a survey of 430 active working adults in the U.S was taken that relates their job satisfaction to their annual income. The results are shown in the contingency table below.

Annual Income Very Satisfied Moderately Satisfied Not Satisfied Total

$100,000 or more 32 4 4 40

$70,000 - $99,999 53 30 12 95

$40,000 - $69,999 84 80 26 190

Less than $40,000 25 37 43 105

Total 194 151 85 430

A) What proportion of the people survey are either 'very satisfied' or 'moderately satisfied'?

B) If one of the 430 people is selected at random, what is the probability that the person makes at least $70,000 annual income?

C) If one of the 430 people is selected at random, and given that the person is not 'very satisfied' with his/her job, what is the probability that the person makes $100,000 or more?