Question

# Which statement best describes the relationship between the sum of squares, the normal distribution, and the...

Which statement best describes the relationship between the sum of squares, the normal distribution, and the chi-squared (x2) distribution?
a. If you square all of the values of a single normally distributed variable and summed all of those squared values (i.e., take the sum of squares), you would have a chi-squared distribution
b. if you squared all of the values of a chi-squared distributed variable and took the sum of those values (i.e., take the sum of squares), you would have a normal distribution
c. if you took the square root of all the values of a normally distributed variable and summed all of those square root values (i.e., take the sum of squares), you would have a chi-squared distribution
d. if you square all of the values of a normally distributed variable and summed all of those squared values (i.e., take the sum of squares), then did this for multiple variables, you would have a chi-squared distribution

d. if you square all of the values of a normally distributed variable and summed all of those squared values (i.e., take the sum of squares), then did this for multiple variables, you would have a chi-squared distribution

Explanation:

Definition of chi square distribution:.

Let X1,…,Xk be independentstandard normal random variables.("Standard normal" means normal with expectation 0 and variance 1.)Then has a chi-square distribution with k degrees of freedom.

Not selected options reasons:

Option a) Here also we can say that it is chi square but only with one degree of freedom as here single variable is used.

Option b) From definition we can not get normal distribution by squaring chi square Variables.

Option c) We need square of normal variable not the square root so this option is also wrong.

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