s there an association between hair color and body type? The table below shows the results of a researcher's observations of randomly selected people. Frequencies of Hair Colors for Various Body Types Blonde Brunette Red Head Short and Slender 73 90 43 Short and Pudgy 110 108 70 Tall and Slender 53 99 70 Tall and Heavy 60 106 78 α = 0.05 significance level The test-statistic for this data = (Please show your answer to three decimal places.) The p-value for this sample = (Please show your answer to four decimal places.) Thus, the final conclusion is... There is sufficient evidence to conclude that hair color and body type are dependent. There is insufficient evidence to conclude that hair color and body type are dependent. There is sufficient evidence to conclude that hair color and body type are independent. There is sufficient evidence to conclude that the distribution of hair color is not the same for each body type. There is insufficient evidence to conclude that the distribution of hair color is not the same for each body type.
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.
Is there an association between hair color and body type? The table below shows the results of a researcher's observations of randomly selected people.
Frequencies of Hair Colors for Various Body Types
| Blonde | Brunette | Red Head | |
|---|---|---|---|
| Short and Slender | 73 | 90 | 43 |
| Short and Pudgy | 110 | 108 | 70 |
| Tall and Slender | 53 | 99 | 70 |
| Tall and Heavy | 60 | 106 | 78 |
α = 0.05 significance level
- The test-statistic for this data = (Please show your answer to three decimal places.)
- The p-value for this sample = (Please show your answer to four decimal places.)
- Thus, the final conclusion is...
- There is sufficient evidence to conclude that hair color and body type are dependent.
- There is insufficient evidence to conclude that hair color and body type are dependent.
- There is sufficient evidence to conclude that hair color and body type are independent.
- There is sufficient evidence to conclude that the distribution of hair color is not the same for each body type.
- There is insufficient evidence to conclude that the distribution of hair color is not the same for each body type.
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