These are a few short answer questions I am stumped on. 1. What is the sampling...

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Statistics

These are a few short answer questions I am stumped on.
1. What is the sampling distribution of the differencebetween means? Why canâ€™t you conduct an independent samples t-testwithout it?
2. What are the assumptions of a two-samplet-test?
3. Why do we â€œpoolâ€ variance for a two-sample t-test?What are the assumptions that make this possible? How does itbenefit us?
5. Why is a confidence interval not a probabilitystatement?
9. What is an effect size? What happens to an effectsize when sample size increases/decreases? Why?
10. What is power? How is it related to the Î±-level,sample size, and effect size?

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ANSWER1 which is the difference between the two populationmeans The variance of the distribution of the sample differencesis equal to Therefore the standard error of thedifferences between two means would be equal to To convert to thestandard normal distribution we use theformulaThe sampling distribution of the difference between means can bethought of as the distribution that would result if we repeated thefollowing three steps over and over again 1 sample n1scores from Population 1 and n2 scores from Population2 2 compute the means of the two samples M1 andM2 and 3 compute the difference between meansM1 M2 The distribution of the differencesbetween means is the sampling distribution of the differencebetween meansAs you might expect the mean of the sampling distribution ofthe difference between means iswhich says that the mean of the distribution of differencesbetween sample means is equal to the difference between populationmeansFor example say that the mean test score of all 12yearolds ina population is 34 and the mean of 10yearolds is 25 If numeroussamples were taken from each age group and the mean differencecomputed each time the mean of these numerous differences betweensample means would be 34 25 9In order to test whether there is a difference betweenpopulation means we are going to make three assumptionsThe two populations have the same variance This assumption See Answer

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