Math Problem Statement

To calculate the 95% confidence interval for the mean using the t-score 𝑡

2.365 t=2.365, follow these steps:

Given Information Sample mean ( 𝑥 ˉ x ˉ ) = 1.250 Sample standard deviation ( 𝑠 s) = 0.080 Sample size ( 𝑛 n) = 8 t-score ( 𝑡 t) = 2.365 (for 7 degrees of freedom and 95% confidence level) Formula The confidence interval (CI) for the mean is calculated as:

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
t-Distribution

Formulas

CI = (xˉ - t * (s / √n), xˉ + t * (s / √n))
Standard Error: SE = s / √n
Margin of Error: t * SE

Theorems

t-distribution
Central Limit Theorem

Suitable Grade Level

Grades 11-12, College Level