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

  1. 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 (i) and (iii) are true.
    D.

    Both (ii) and (iii) are true.
Math   Statistics-And-Probability   
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Answer #1

Answer: D. Both (ii) and (iii) are true

When estimating a confidence interval for the difference between the means of two independent populations the following assumptions are made:

  • The variances of the two populations are equal.
  • The two samples are independent. There is no relationship between the individuals in one sample as compared to the other.
  • Both samples are simple random samples from their respective populations. Each individual in the
    population has an equal probability of being selected in the sample.
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