Suppose you are conducting a two-sample t-test and have two sample sizes: n1=10n_1=10 and n2=15n_2=15. Using the conservative approach, you use degrees of freedom equal to the minimum of n1−1n_1-1 and n2−1n_2-1, which is 99. This gives a critical value of t=2.262t=2.262 for a one-tailed test at the 0.050.05 significance level. If you instead use the formula for degrees of freedom and get 17.817.8, the critical value is t=1.740t=1.740. Why is using t=2.262t=2.262 considered more conservative than t=1.740t=1.740?

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Problem 10Multiple Choice

Suppose you are conducting a two-sample t-test and have two sample sizes: $n sub 1 equals 10$ and $n sub 2 equals 15$ . Using the conservative approach, you use degrees of freedom equal to the minimum of $n sub 1 minus 1$ and $n sub 2 minus 1$ , which is $9$ . This gives a critical value of $t equals 2.262$ for a one-tailed test at the $0.05$ significance level. If you instead use the formula for degrees of freedom and get $17.8$ , the critical value is $t equals 1.740$ . Why is using $t equals 2.262$ considered more conservative than $t equals 1.740$ ?

Because a larger critical value requires stronger evidence to reject the null hypothesis.

Because a smaller critical value makes it easier to reject the null hypothesis.

Because it increases the probability of a Type I error.

Because it uses more information from both samples.

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