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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 endpoints of the t-distribution with $2.5 %$ beyond them in each tail if the samples have sizès $n_{1} = 17$ and $n_{2} = 25$ .
Enter the exact answer for the degrees of freedom and round your answer for the endpoints to two decimal places.
$\begin{array}{l} degrees of freedom = \bar{i} \\ endpoints = \pm i \end{array}$

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So, the final answer is: degrees of freedom = $40$ , endpoints = $\pm 2.02$

Steps

Step 1 ：Calculate the degrees of freedom using the formula: $d f = n 1 + n 2 - 2$

Step 2 ：Substitute the given values into the formula: $d f = 17 + 25 - 2$

Step 3 ：Simplify the equation to find the degrees of freedom: $d f = 40$

Step 4 ：Find the endpoints of the t-distribution with 2.5% beyond them in each tail. For a t-distribution with 40 degrees of freedom, the t-value that leaves 2.5% in each tail (or 5% total in both tails) is approximately ±2.021

Step 5 ：So, the final answer is: degrees of freedom = $40$ , endpoints = $\pm 2.02$

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