The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are $n _ { 1 } = 9 \text { and } n _ { 2 } = 10$ How many degrees of freedom did the calculator use?
A) 16.933567
B) 15.933567
C) 0.001964
D) -3.366473

Question

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are $n _ { 1 } = 9 \text { and } n _ { 2 } = 10$ How many degrees of freedom did the calculator use?
A) 16.933567 
B) 15.933567 
C) 0.001964 
D) -3.366473

Quizplus · Accepted Answer

The calculator used a t-test to compare the means, which requires the degrees of freedom to be calculated as $df = n_1 + n_2 - 2$. Substituting $n_1=9$ and $n_2=10$, we get $df = 9 + 10 - 2 = 17 - 2 = 15$. Therefore, the calculator used 15 degrees of freedom. Option B is the closest to the correct value. Options A and D are too large to be reasonable, and option C is much too small.

The Following Display from a TI-84 Plus Calculator Presents the Results