Question

find the t - value for the given values of x, μ, s, and n.
x = 65.6, μ = 62.4, s = 7.2, n = 12
t = □ (round to two decimal places as needed)

Explanation:

Step1: Recall the t - value formula

The formula for the t - value is \(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\)

Step2: Substitute the given values

Given \(\bar{x} = 65.6\), \(\mu=62.4\), \(s = 7.2\), \(n = 12\)

First, calculate the numerator: \(\bar{x}-\mu=65.6 - 62.4=3.2\)

Second, calculate the denominator: \(\frac{s}{\sqrt{n}}=\frac{7.2}{\sqrt{12}}\approx\frac{7.2}{3.464}\approx2.08\)

Then, \(t=\frac{3.2}{2.08}\approx1.54\)

Answer:

\(t = 1.54\)