Question

find the t - value for the given values of \\( \overline { x } \\), \\( \mu \\), s, and n. \\( \overline { x } = 70.2, \mu = 64.2, s = 7.9, n = 24 \\) \\( t = \square \\) (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 \(\bar{x} = 70.2\), \(\mu=64.2\), \(s = 7.9\), \(n = 24\)

First, calculate \(\bar{x}-\mu\): \(70.2-64.2=6\)

Then, calculate \(\frac{s}{\sqrt{n}}\): \(\frac{7.9}{\sqrt{24}}\approx\frac{7.9}{4.899}\approx1.6126\)

Step3: Calculate the t - value

\(t=\frac{6}{1.6126}\approx3.72\)

Answer:

\(3.72\)