Question

# Consider the following statements. When estimating a confidence interval for the difference between the means of...

Consider the following statements. When estimating a confidence interval for the difference between the means of two independent populations. (i) The variances in both populations of variable X are assumed to be zero. (ii) Samples should be independently and randomly selected from the populations. (iii) Both samples have the same variance. A. Only (ii) is true. B. Only (i) is true. C. Both (ii) and (iii) are true. D. Both (i) and (iii) are true.

Solution:- C. Both (ii) and (iii) are true.

(i) The variances in both populations of variable X are assumed to be zero. False

(ii) Samples should be independently and randomly selected from the populations. True

(iii) Both samples have the same variance. True

For a confidence interval to be valid, numbers of assumptions are made as follows:

1) The two population we samples are normal.

2) The two population have the same variances.

3) The two samples are random samples from the population of interest.

4) The two samples are independent.

Hence from the above assumptions Both (ii) and (iii) are true.

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