Suppose we compute a 95percent interval for 1-2. If the interval is: A) (3,5) ca

Question

Suppose we compute a 95percent interval for 1-2. If the interval is:
A) (3,5) can we be 95% confident that 1 is greater than 2?Why or why not?
B) (3,5) can we be 95% confident that 1 is not equal to 2?Why or why not?
C) (-20.-10) can we be 95% confident that 1 is not equal to2? Why or why not?
D) (-20,-10) can we be 95% confident that 1 is greater than2? Why or why not?
E) (-3,2) can we be 95% confident that 1 is not equal to 2?Why or why not?
F) (-10,10) can we be 95% confident that 1 is less than 2?Why or why not?
G) (-10,10) can we be 95% confidnet that 1 is greater that2? Why or why not?

Explanation / Answer

Wherever the 95% confidence interval contains zero, we cannot besure that the difference is significant. This is because a zerodifference between the two scores falls within the realm ofpossibilities that we are able to consider to be 95% likely. Hence: A: Yes - interval doesn't contain zero, and the difference ispositive B: Yes - interval doesn't contain zero C: Yes - interval doesn't contain zero D: No - in fact, we can be 95% confident that 2 is greaterthan 1 as the difference is negative E: No - interval contains zero F: No - the confidence interval contains positive values (i.e.between 0 and 10) - these fall within the 95% realm ofprobability G: No - the confidence interval contains negative values (i.e.between -10 and 0) - these fall within the 95% realm of probability

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