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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.
School system A school district superintendent wants to
test a new method of teaching arithmetic in the fourth grade
at his 15 schools. He plans to select 8 students from each
school to take part in the experiment, but to make sure they
are roughly of the same ability, he first gives a test to all
120 students. Here are the scores of the test by school:The ANOVA table shows:
Source DF
Sum of
Squares
Square F-Ratio P-Value
School 14 108.800 7.7714 1.0735 0.3899
Error 105 760.125 7.2392
Total 119 868.925a) What are the null and alternative hypotheses?
b) What does the ANOVA table say about the null
hypothesis? (Be sure to report this in terms of scores
and schools.)
c) An intern reports that he has done t-tests of every
school against every other school and finds that several
of the schools seem to differ in mean score. Does this
match your finding in part b? Give an explanation for
the difference, if any, of the two results.
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