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When we do a t-test, the critical value is pushed out farther and farther into the tails because the area in a t-distribution is

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When we do a t-test, the critical value is pushed out farther and farther into the tails because the area in a t-distribution is fatter than a z-distribution in the tails. What is the major disadvantage to pushing the critical value farther out when using the t-test?

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