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(e) The distribution of each random variable on the left matches with a distribution on the right, and no distribution on the
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Answer #1

i.) The correct match is a. t32  

i.e. Students t distribution with 32 degrees of freedom.

ii.) The correct match is c. t31   

as the test statistic given, would follow student's t-distribution with 20+14-2 degrees of freedom i.e. 31 degrees of freedom.

iii.) The correct match is d. t57

iv.) The correct match is e. χ210

As the statistic is the sum of the squares of 10 standard normal variates.

v.) The correct match is b. F8,12   

The statistic is the ratio of independent standard normal variate and chi-square variant divided by the degrees of the freedom F distribution.

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