Final answer:
The critical value for a two-tailed t-test at a 0.05 significance level with 27 degrees of freedom is approximately ±2.055. The closest answer given is a) ±2.056.
Step-by-step explanation:
You asked for the critical value of a one-sample hypothesis test for the mean, μ, at a significance level of 0.05, given a test statistic of 2.5 and 27 degrees of freedom. To find the critical value for a two-tailed test at a significance level (α) of 0.05 with 27 degrees of freedom, we need to refer to a t-distribution table or use software to determine the critical t-value. For 27 degrees of freedom, the critical t-value that corresponds to a significance level of 0.05 is approximately ±2.055 or ±2.056 if you round up slightly. Since none of the provided options exactly matches this, the closest answer would be a) ±2.056. However, if it's a one-tailed test, the critical value may differ slightly. Remember, to determine whether to reject the null hypothesis or not, you would compare the calculated test statistic to the critical value.