In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the 300 students in the class. After the exam, 6 students from the class got together and petitioned to nullify the results on the grounds that the four versions were not equal in difficulty. To investigate the students' assertion, the professor examined the means and variances of the scores on the different versions of the exam, obtaining the following information (the exam had 200 possible points). Sample Sample Sample Group size mean variance Version A 75 156.8 351.7 Version B 75 155.7 493.5 Version C 75 159.0 450.3 Version D 75 149.6 337.9 Send data to calculator Taking the 75 scores for each version of the exam as a sample of scores for that version, the professor performed a one-way, independent-samples ANOVA test of the equality of the population mean scores for the four versions. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) What is the value of the "between groups" mean square that would be reported in the ANOVA test? (b) What is the value of the "within groups" mean square that would be reported in the ANOVA test?
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.
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