Question

Consider the following statements.

(i). If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

(ii). If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.

(iii). The critical value of t for a two-tail test of the difference of two means, a level of signifi- cance of 0.10 and sample sizes of seven and fifteen, is ±1.734.

Which of the following is true?

A. (i), (ii), and (iii) are all correct statements.

B. (i), (ii), and (iii) are all false statements.

C. (i) and (ii) are correct statements but not (iii).

D. (i) and (iii) are correct statements but not (ii). E. (ii) and (iii) are correct statements but not (i).

Answer 1

Answer:

(i) and (ii) are correct statements but not (iii)

Explanation:

(i) If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

This statement is correct statement.

(ii) If we are testing for the difference between two population means, it is assumed that the two populations are approximately normal and have equal variances.

This staement is correct statement.

(iii). Here

n1 = 7

n2 = 15

degrees of freedom (df) = n1+n2-2

df = 7+15-2

df = 22-2

df = 20

For a two- tailed test

t critical = t ,df

t -critical = t 0.10,20

t critical =   1.725

Therefore

The critical value of t for a two-tail test of the difference of two means, a level of signifi- cance of 0.10 and sample sizes of seven and fifteen, is ±1.734 is wrong statement

So, the answer is  (i) and (ii) are correct statements but not (iii)

Hence the "option- C" is the correct answer.