Find the critical value and rejection region for the type of t-test with level of significance α $\alpha$ and sample size n. Two-tailed test, α $\alpha$ = 0.05, n = 38 A) $\mathrm { t } _ { 0 } = - 2.026 , \mathrm { t } _ { 0 } = 2.026 ; \mathrm { t } 2.026$ B) $\mathrm { t } _ { 0 } = - 2.024 , \mathrm { t } _ { 0 } = 2.024 ; \mathrm { t } 2.024$ C) $t _ { 0 } = 2.026 ; t 2.026$ D) $t _ { 0 } = - 1.687 , t _ { 0 } = 1.687 ; t 1.687$

Question

Find the critical value and rejection region for the type of t-test with level of significance α $\alpha$ and sample size n. Two-tailed test, α $\alpha$ = 0.05, n = 38 A) $\mathrm { t } _ { 0 } = - 2.026 , \mathrm { t } _ { 0 } = 2.026 ; \mathrm { t } < - 2.026 , \mathrm { t } > 2.026$ B) $\mathrm { t } _ { 0 } = - 2.024 , \mathrm { t } _ { 0 } = 2.024 ; \mathrm { t } < - 2.024 , \mathrm { t } > 2.024$ C) $t _ { 0 } = 2.026 ; t > 2.026$ D) $t _ { 0 } = - 1.687 , t _ { 0 } = 1.687 ; t < - 1.687 , t > 1.687$

Quizplus · Accepted Answer

For a two-tailed t-test with α = 0.05 and n = 38, the degrees of freedom (df) is n - 1 = 37. Looking up the critical value in a t-distribution table for df = 37 and α/2 = 0.025 (since it's two-tailed), the closest value is typically around 2.026. This means the rejection regions are t < -2.026 and t > 2.026.

Find the Critical Value and Rejection Region for the Type α\alphaα

Find the Critical Value and Rejection Region for the Type $\alpha$