Question

find the standardized test statistic t for a sample with n = 12, \\( \overline { x } = 23.2 \\), s = 2.2, and \\( \alpha = 0.01 \\) if \\( h _ { 0 } : \mu = 22 \\). round answer to two decimal places.

a. 2.00
b. 2.13
c. 1.99
d. 1.89

Explanation:

Step1: Recall the formula for t - statistic

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

Step2: Substitute the given values

We are given that \(\bar{x} = 23.2\), \(\mu=22\), \(s = 2.2\), and \(n = 12\)

First, calculate \(\frac{s}{\sqrt{n}}\):
\(\frac{s}{\sqrt{n}}=\frac{2.2}{\sqrt{12}}\approx\frac{2.2}{3.464}\approx0.635\)

Then, calculate \(t\):
\(t=\frac{23.2 - 22}{0.635}=\frac{1.2}{0.635}\approx1.89\)

Answer:

D. 1.89