Available after Friday, November 17, 2017 12:00 AM MST. Unlocked: Friday, Novemb

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Available after Friday, November 17, 2017 12:00 AM MST. Unlocked: Friday, November 17, 2017 12:00 AM MST - Friday, December 1, 2017 11:00 PM MST. Must post first. Welcome to your last graded discussion board for the course!! Please engage with your classmates to help one another clarify and solidify another often fuzzy topic. For this discussion, please focus on testing the difference between means for two independent samples versus two dependent samples. In particular, Sections 8.1 and 8.2 covered details about testing the difference between means for two independent samples, whereas Section 8.3 covered details about testing the difference between means of two samples that are dependent. So, what is the difference, both in how to categorize such a hypothesis test and how to execute it? If you were not aware of what section of the book a question came from, then how would you be able to determine if you are looking at independent or dependent samples? Are there key words or phrases that give it away? Why does it matter whether the samples are independent or dependent? How are the details of the hypothesis test different in each case?

Explanation / Answer

Answer:

For checking the statistically significant difference between two population means, we use the t test for population means. When given two samples are independent from each other, then we use independent samples t test and when two samples are dependent, then we use paired t test. For independent samples, there is no any relationship between two samples and observations are independents. In dependent samples, observations are not independent and these observations are related to each other. Observations from the same subject are taken at two different times. Sometimes, it is called as before-after data relationship. In paired t test we use paired data. In independent samples t test, the sample sizes would be different for given two samples, however sample sizes are same in paired t test as observations in samples are one to one related.

For independent samples t test, we use two sample t test assuming equal or unequal population variance. The test statistic used for this test is given as below:

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

Where Sp2 is pooled variance

Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

For paired t test, we use the test statistic given as below:

t = Dbar / [Sd/sqrt(n)]

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