A sample of 15 students took a calculus test, and the average score was 70 with a standard deviation of 10. What is the t-value for the 95% confidence level?
Answer
Step 3: Find the t-value that corresponds to this area in the t-distribution table. Looking up 14 degrees of freedom and 2.5% in the t-distribution table, we find the t-value of 2.145.
Step 1 ：Step 1: Identify the degrees of freedom. The degrees of freedom is equal to the sample size minus 1, which is \(15 - 1 = 14\).
Step 2 ：Step 2: Identify the confidence level. The confidence level is 95%, which leaves 5% in the two tails of the distribution. So, the area in each tail is \(\frac{5}{2} = 2.5\%\).
Step 3 ：Step 3: Find the t-value that corresponds to this area in the t-distribution table. Looking up 14 degrees of freedom and 2.5% in the t-distribution table, we find the t-value of 2.145.
