Answer to 4 decimal places 4. Answer the following questions with TRUE or FALSE.

Question

Answer to 4 decimal places

4. Answer the following questions with TRUE or FALSE. (a) A Goodness of Fit test with two categories (k = 2) (b) You can perform a one-sided hypothesis test on a (c) The calculation of the 2 test-statistic for a Test for It is good practice to explain your answers. must test a one-sided hypothesis. categorical variable that has 4 categories. Independence does not change if you are testing a one-sided alternative (d) When you are testing if the probability of being in k categories of a categorical variable is equal, pi for all i 1/k

Explanation / Answer

a) The test of goodness of fit is done by using the statistic chi sqare. The value of this statistic cannot be negative. That is, the curve is extended towards right, not left. So, the alternative hypothesis is always one sided (righ sided). Hence, the ststement is true.

b) We can perform a one sided hypothesis test on four categorial variables by using only chi square test statistic, but not always by other parametric and non parametric test statistic. Hence, the statement is false

c) The value of the chi square test statistic is always positive and it is always a one sided test (right). Hence, the statement is true.

d) Here, our null hypothesis H0 : All the categories are equally distributed i.e. the probability of each of the k categories is 1/k. Hence, the statement is true.

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