What is the probability that a randomly chosen employee
1. Text book problems to complete Chapter Four Work: p. 173; 4.37
4.37 G2 Crowd provides commentary and insight about employee engagement trends and challenges within organizations in its G2 Crowd Employee Engagement Report. The report represents the results of an online survey conducted in 2019 with employees located across the United States. G2 Crowd was interested in examining differences between HR and non-HR employees. One area of focus was on employees’ response to important metrics to consider when evaluating the effectiveness of employee engagement programs. The findings are summarized in the following tables.
What is the probability that a randomly chosen employee
Source: Data extracted from “Employee Engagement,” G2 Crowd, bit.ly/2WEQkgk
PRESENTEEISM IS AN IMPORTANT METRIC | |||
EMPLOYEE | Yes | No | Total |
HR | 53 | 79 | 132 |
Non-HR | 43 | 225 | 268 |
Total | 96 | 304 | 400 |
ABSENTEEISM IS AN IMPORTANT METRIC | |||
EMPLOYEE | Yes | No | Total |
HR | 54 | 78 | 132 |
Non-HR | 72 | 196 | 268 |
Total | 126 | 274 | 400 |
What is the probability that a randomly chosen employee
a. is an HR employee?
b. is an HR employee or indicates that absenteeism is an important metric to consider when evaluating the effectiveness of employee engagement programs?
c. does not indicate that presenteeism is an important metric to consider when evaluating the effectiveness of employee engagement programs and is a non-HR employee?
d. does not indicate that presenteeism is an important metric to consider when evaluating the effectiveness of employee engagement programs or is a non-HR employee?
e. Suppose the randomly chosen employee does indicate that presenteeism is an important metric to consider when evaluating the effectiveness of employee engagement programs. What is the probability that the employee is a non-HR employee?
f. Are “presenteeism is an important metric” and “employee” independent?
g. Is “absenteeism is an important metric” independent of “employee”?
2. Non-text book problems to complete:
Use the following information to answer the next two questions.
Many people like to shop in person, then make their purchase later, online. Of all the shoppers, it was found that 30% of shoppers make purchases when they physically enter a store. Some retailers offer promotions to attempt to track customers purchasing using the process of looking then ordering online. Retailers started to offer customers, when leaving the building without making a purchase, a discount code to use for online purchases. It was found that there’s a 9% chance of a person making a purchase using the code later.
A. What is the probability that a shopper who enters the building will not make any purchases?
B. Retailers noticed when two shoppers enter the building to shop together (the purchases are not disjoint), there is a 20% chance they both will make a purchase. What is the probability that at least one of them makes a purchase?
C. You would like to “build-your-own-burger” at a fast-food restaurant. There are five different breads, seven different cheeses, four different cold toppings, and five different sauces on the menu. If you want to include one choice form each of these ingredient categories, how many different burgers can you build?
D. If P(B) = 0.05, P(A|B) = 0.80, P(B’) = 0.95, and P(A|B’) = 0.40, find P(B|A).
E. How many different ways can a senior project manager and an associate project manager be selected for an analytics project if there are eight data scientists available?
F. Texting while driving is a problem. Maryland Department of Motor Vehicles commissioned a study and found on average 400 accidents occur on the DC beltway every two weeks. The data is given next:
Number of Vehicles Involved in the Accident | ||||
Texting while Driving | 1 | 2 | 3 | |
Yes | 50 | 100 | 20 | 170 |
No | 25 | 175 | 30 | 230 |
75 | 275 | 50 | 400 |
What proportion of accidents involved more than one vehicle?
What proportion of accidents involved texting and a single vehicle?
Given that multiple vehicles were involved, what proportion of accidents involved texting?
Given that 3 vehicles were involved, what proportion of accidents involved texting?
G. True or False. If false, be sure to include why it is false!
1. If either A or B must occur they are called mutually exclusive.
2. If P(A) = 0.4 and the P(B) = 0.5, then A and B must be collectively exhaustive.
3. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P(A and B) = 0.1. Then P(A|B) = 0.4
Discussion
Please pick one topic or term, from the textbook content in Chapter Four, that was most interesting or difficult or relevant to you. Post on the discussion board the topic or statistics term and what you were thinking about this topic or statistics term. Include a summary of the topic or term, perhaps include an example, or a diagram – or another website or video about the topic, etc. Be creative! (This is meant to be an open discussion that can go in numerous directions.) Examples for topics or statistical terms could be (but not limited to): empirical probability, marginal probability joint probability, multiplication rule, Bayes’ theorem, combinations, permutations, independence, mutually exclusive, etc. The word count should be at least 150 words. The topic is 4.4 Bayes’ Theorem
Developed by Thomas Bayes in the eighteenth century, Bayes’ theorem builds on conditional probability concepts that Section 4.2 discusses. Bayes’ theorem revises previously calculated probabilities using additional information and forms the basis for Bayesian analysis. (Anderson-Cook, Bellhouse, Hooper).
In recent years, Bayesian analysis has gained new prominence for its application to analyzing big data using predictive analytics (see Chapter 17). However, Bayesian analysis does not require big data and can be used in a variety of problems to better determine the revised probability of certain events. The Bayesian Analysis online topic contains examples that apply Bayes’ theorem to a marketing problem and a diagnostic problem and presents a set of additional study problems. The Consider This for this section explores an application of Bayes’ theorem that many use every day, and references Equation (4.9) that the online topic discusses.