Question

Which of the following critical values is largest? (You should be able to answer this question without actually calculating any of these critical values.)

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a. t₁₀.₀.₀₂₅
b. t₂₀,₀.₀₂₅
c. Z₀.₀₂₅
d. Z₀.₀₅

Answer 1

The largest critical value is t20,0.025.

Step-by-step explanation:

To determine which of the given critical values is the largest, we need to compare the values for t-distribution and z-distribution. The t-distribution critical values, t10.0.025 and t20,0.025, represent the values for confidence level 95% and sample sizes 10 and 20 respectively. The z-distribution critical values, Z0.025 and Z0.05, represent the values for confidence level 95% and 99% respectively.

Since we know that the t-distribution has thicker tails compared to the z-distribution, the larger critical values will be for the t-distribution. Therefore, the largest critical value is t20,0.025 (option b).