Which of the following statements are true concerning the mean of the difference

Question

Which of the following statements are true concerning the mean of the differences between two dependent samples (matched pairs)? Select all that apply. A. The requirement of a simple random sample is satisfied if we have independent pairs of convenience sampling data. B. The methods used to evaluate the mean of the differences between two dependent variables apply if one has 30 IQ scores of voters from California and 30 IQ scores of voters from Texas. C. If one has more than 8 matched pairs of sample data, one can consider the sample to be large and there is no need to check for normality. D. If one has fifteen matched pairs of sample data, there is a loose requirement that the fifteen differences appear to be from a normally distributed population. E. If one wants to use a confidence interval to test the claim that mu_d > 0 with a 0.10 significance level, the confidence interval should have a confidence level of 80%.

Explanation / Answer

The 'nearly normal' assumption for matched pair is robust and is true if the sample size is 15 or less for samples drawn from a population which is normal (symmetric, unimodal and without outlier). It holds true for sample size greater than 15 drawn from a population which is slightly skewed, but roughly symmetric and without any outlier.

Therefore, option C and D.

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