You volunteer some of your spare time to your local fire department and have been asked by an assistant chief to analyze data on firefighters who applied for promotion. The assistant chief wants to ensure that gender bias is not a concern in the promotion of firefighters. Shown below is data for 50 firefighters who applied for promotion and the results of a chi-square analysis of the data. Male Female Promoted 13 22 Not Promoted 10 5 Chi-Square Statistic 3.6845 P value 0.054919 Is the promotional status of recently promoted firefighters independent of their gender? What reasons should the assistant chief convey to the fire chief to justify the absence of gender bias in the most recent class of firefighters who were promoted?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
You volunteer some of your spare time to your local fire department and have been asked by an assistant chief to analyze data on firefighters who applied for promotion. The assistant chief wants to ensure that gender bias is not a concern in the promotion of firefighters. Shown below is data for 50 firefighters who applied for promotion and the results of a chi-square analysis of the data.
|
Male |
Female |
|
|
Promoted |
13 |
22 |
|
Not Promoted |
10 |
5 |
|
Chi-Square Statistic |
3.6845 |
|
P value |
0.054919 |
|
|
|
- Is the promotional status of recently promoted firefighters independent of their gender?
- What reasons should the assistant chief convey to the fire chief to justify the absence of gender bias in the most recent class of firefighters who were promoted?
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