Question

____________ is a test of a single population and is to determine if there is an association between two characteristics of that population.

A)  The chi-square test for independence

B)  Pearson product moment test

C)  The chi-square test for homogeneity

D)  Goodness-of-fit test

E)  Welch’s t test

9)   ____________ is a test to determine if two distinct populations are the same with respect to a single characteristic, i.e. if that characteristic is exhibited by the same percentage of the two populations.

A)  The chi-square test for independence

B)  Goodness-of-fit test

C)  The chi-square test for homogeneity

D)  The Behrens-Fisher test

E)  Pearson product moment test

10) The procedures and assumptions for the chi-square test for independence and the chi-square test for homogeneity are the same.

A)  True

B)  False

11) A variable that is chi-square distributed can take positive or negative values.

A)  True

B)  False

12) The idea behind the chi-square test for independence is to compare actual counts to the counts we would expect if the null hypothesis were true (if the variables are independent).  If a significant difference between the actual counts and expected counts exists, we would take this as evidence against the null hypothesis.

A)  True

B)  False

13) If two events are independent, then the probability of events X and Y equals the probability of event X times the probability of event Y.

A)  True

B)  False

Answer 1

8) (A) The chi-square test for independence.

option (B) and (E) are two-sample tests.(C) involves two attributes. (D) Doesn't cjheck association. Hence all these are incorrect.

9) D)  The Behrens-Fisher test

In this test, the difference between the means of two independent normally distributed populations is tested to be equal to 0 for the case where the variances of the two populations are not assumed to be equal.

10) A) TRUE

The chi-square test for independence as well as the chi-square test for homogenity compares the observed frequency and the expected frequency for each of the class the variable belongs to.

11) B) FALSE

A chi-square random variable can take only positive values.

12) A) TRUE

The given statement is indeed the idea behind the chi-square test for independence, as explained in Que.10) also.

13) A) TRUE

As per the definition of independence of two random variables,

P(X=x,Y=y) = P(X=x)*P(Y=y) for all (x,y) in the sample space.

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