Suppose that $\bar{x}=81$ is being used as an estimate of the true average score for students' first exam in psychology. What can be said with $95 \%$ confidence about the maximum error if $n=11$ and $s=5$ ?
A) $E \approx 2.73$
B) $E \approx 3.32$
C) $E \approx 3.36$
D) $E \approx 2.71$

Question

Quizplus · Accepted Answer

The maximum error of the estimate, $E$, is calculated using the formula $E = t_{\alpha/2} \times \frac{s}{\sqrt{n}}$. For $n=11$, the degrees of freedom is $10$. Using a t-distribution table, $t_{0.025}$ for 10 degrees of freedom is approximately 2.228. Thus, $E = 2.228 \times \frac{5}{\sqrt{11}} \approx 3.36$.

Suppose That xˉ=81\bar{x}=81xˉ=81 Is Being Used as an Estimate of the True Average

Suppose That $\bar{x}=81$ Is Being Used as an Estimate of the True Average