Question

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evaluate the formula ( t=\frac{\bar{x}-mu}{\frac{s}{sqrt{n}}} ) when ( mu = 126 ), ( n = 21 ), ( \bar{x}=124 ), and ( s = 7 ).
( t=quad ) (round to three decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Substitute \(\mu = 126\), \(\bar{x}=124\), \(s = 7\), and \(n = 21\) into \(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\).

$$t=\frac{124 - 126}{\frac{7}{\sqrt{21}}}$$

Step2: Calculate the numerator

Calculate \(124−126=- 2\).

Step3: Calculate the denominator

First, calculate \(\sqrt{21}\approx4.5837\). Then \(\frac{7}{\sqrt{21}}=\frac{7}{4.5837}\approx1.5272\).

Step4: Calculate the value of \(t\)

\(t=\frac{-2}{1.5272}\approx - 1.31\)

Answer:

\(-1.31\)