1. In at least 6 sentences discuss a situation where you would test for independence. The Chi-Square test of independence is used to determine a significant relationship between two nominal (categorical) variables. The frequency of each category for one nominal variable is compared across the categories of the second nominal variable. The data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable. In the test of independence, observational units are collected at random from a population and two categorical variables are observed for each unit. In the test of homogeneity, the data are collected by randomly sampling from each sub-group separately. 2. In at least 6 sentences discuss a situation where you would test for homogeneity. The Chi-Square-homogeneity test is used to compare the distribution of the variable for two or more populations. The null hypothesis for this test states that the distribution of the variables is the same for all the population, whereas the alternative hypothesis states that the distribution is different for at least two populations. If the populations under consideration have the same distribution for a variable, they are known as homogeneous with respect to the variable. Whereas if the distribution is not the same, then they are known as non homogeneous with respect to the variable. 3. Find a real life example of each.
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.
1. In at least 6 sentences discuss a situation where you would test for independence.
The Chi-Square test of independence is used to determine a significant relationship between two nominal (categorical) variables.
The frequency of each category for one nominal variable is compared across the categories of the second nominal variable.
The data can be displayed in a
In the test of independence, observational units are collected at random from a population and two categorical variables are observed for each unit. In the test of homogeneity, the data are collected by randomly sampling from each sub-group separately.
2. In at least 6 sentences discuss a situation where you would test for homogeneity.
The Chi-Square-homogeneity test is used to compare the distribution of the variable for two or more populations.
The null hypothesis for this test states that the distribution of the variables is the same for all the population, whereas the alternative hypothesis states that the distribution is different for at least two populations.
If the populations under consideration have the same distribution for a variable, they are known as homogeneous with respect to the variable. Whereas if the distribution is not the same, then they are known as non homogeneous with respect to the variable.
3. Find a real life example of each.
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