Question

​Which of the following sets of data would produce the largest value for an independent-measures t statistic? ​The two sample means are 10 and 20 with variances of 20 and 25 ​The two sample means are 10 and 20 with variances of 120 and 125 ​The two sample means are 10 and 12 with sample variances of 20 and 25 ​The two sample means are 10 and 12 with variances of 120 and 125

Answer 1

Answer:

The two sample means are 10 and 12 with variances of 20 and 25

Step-by-step explanation:    

The formula used for t-statistics is:

     $t=\frac{\bar{x_{1}}-\bar{x_{2}} }{\sqrt{\frac{s_{1}^2}{n_{1}}+\frac{s_{2}^2}{n_{2}}  }}$

Thus t is inversely proportional to s² i.e. variance.

Hence for larger value of variance, we get small value of t-statistics and vice-versa.

Thus for produce the largest value for an independent-measures t statistic, the two sample means are 10 and 20 with variances of 20 and 25.

Answer 2

Answer:

The two sample means are 10 and 20 with variances of 20 and 25 produce the largest value for an independent-measures t statistic.

Explanation:

Option A : The two sample means are 10 and 20 with variances of 20 and 25.

$s_{M_{1}-M_{2}}=\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}$

$=\sqrt{\frac{20}{10}+\frac{25}{10}}$

$=\sqrt{2+2.5}$

$=\sqrt{4.5}$

$=2.12$

$t=\frac{M_{1}-M_{2}}{s_{M_{1}-M_{2}}}$

$=\frac{10-20}{2.12}$

$=\frac{-10}{2.12}$

$=-4.72$

The two sample means are 10 and 20 with variances of 20 and 25 produce the largest value for an independent-measures t statistic.

Learn more about sample mean, refer:

https://brainly.com/question/18060320