Read the options to question 1 carefully and choose the correct choice. 1. Which

Question

Read the options to question 1 carefully and choose the correct choice. 1. Which of the following is false? (4 points) a. We use two sided t-test when we are checking if the averages of the two variables are different, with no prior assertion on which is larger of the two. b. We use one sided t-test when we are checking if the averages of the two variables are different, but now we are more specific. We want to show that X has a significantly larger/smaller average than Y. c. We need to perform the averages of the two variables data set when one sided t-test is chosen in order to see if the averages are consistent with the claim. d. The one sided t-test and two sided t-test performed on the same data sets should return the same P-value. e. The P-value excel returns on a one sided t-test is incorrect and meaningless if the averages computed on the data sets are inconsistent with the claim.

Explanation / Answer

The false option is,

The one sided t-test and two sided t-test performed on the same data sets should return the same P-value.

To show the proof for above statement, we give a counter example.

Here we consider the two samples of each have same size 10. Samples are given as follows,

Now by using Excel function we perform t test for equality of two sample means using and calculate one sided and two sided p value is as follows.

1) One sided t-test with equal variance:-

Excel function:- TTEST(X,Y,1,2) and we get output is 0.000156

2) Two sided t-test with equal variance:-

Excel function:- TTEST(X,Y,2,2) and we get output is 0.000312

Hence the proof.

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