In: Statistics and Probability
Given a data set with 100 observations, a goodness of fit test to see if a sample follows a uniform distribution or a poisson distribution or a normal distribution will have the same number of degrees of freedom. true or false
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When a contingency table of expected frequencies is constructed, the null hypothesis is that all of the cells in the table are equally likely. true or false
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Given a data set with 100 observations, a goodness of fit test to see if a sample follows a uniform distribution or a poisson distribution or a normal distribution will have the same number of degrees of freedom.
Answer: True
Explanation: The above statement is true, because the degrees of freedom will be depends upon how many bins we will use for the given 100 observations. For example, if we use 5 bins for the given data, then degrees of freedom will be 4. There is no any effect of the type of the distribution on the degrees of freedom, but we decide degrees of freedom or bins based on shape of the given data.
When a contingency table of expected frequencies is constructed, the null hypothesis is that all of the cells in the table are equally likely.
Answer: True
Under the null hypothesis for the chi square test for the independence between two categorical variables, we assume that the all cells in the contingency table are equally likely.