Question

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the proportion in a t-distribution less than -1.4 if the samples have sizes n1

Answer 1

Answer:

The degrees of freedom is 11.

The proportion in a t-distribution less than -1.4 is 0.095.

Step-by-step explanation:

The complete question is:

Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably normally distributed, and that a t-statistic will be used for inference about the difference in sample means. State the degrees of freedom used. Find the proportion in a t-distribution less than -1.4  if the samples have sizes 1 = 12 and n 2 = 12 . Enter the exact answer for the degrees of freedom and round your answer for the area to three decimal places. degrees of freedom = Enter your answer; degrees of freedom proportion = Enter your answer; proportion

Solution:

The information provided is:

$n_{1}=n_{2}=12\\t-stat=-1.4$

Compute the degrees of freedom as follows:

$\text{df}=\text{Min}.(n_{1}-1,\ n_{2}-1)$

   $=\text{Min}.(12-1,\ 12-1)\\\\=\text{Min}.(11,\ 11)\\\\=11$

Thus, the degrees of freedom is 11.

Compute the proportion in a t-distribution less than -1.4 as follows:

$P(t_{df}$

                      $=P(t_{11}>1.4)\\\\=0.095$

*Use a t-table.

Thus, the proportion in a t-distribution less than -1.4 is 0.095.