Question

Step 2: In the question above, find (using the method of your choice—formula, or graphing calculator function, or Excel, or app) the value of the test statistic t, to two places after the decimal point.

Answer 1

From the question given,

The formula to find the test statistics mean is given below as,

`t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}`

Where,

`\begin{gathered} \bar{x}\text{ is the population mean} \\ \mu\text{ is the sample mean} \\ \sigma\text{ is the standard deviation } \\ n\text{ is the }sample\text{ size} \end{gathered}`

Given the values of the above below,

`\begin{gathered} \bar{x}=2.27\text{ mins} \\ \mu=2.98\text{ mins} \\ \sigma=0.98\text{ mins} \\ n=20 \end{gathered}`

Substituting the values into the formula of test statistics t above,

`\begin{gathered} t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}} \\ t=\frac{2.27-2.98}{\frac{0.98}{\sqrt[]{20}}}=(-0.71)/((0.98)/(4.472))=-(0.71)/(0.219)=-3.242 \\ t=-3.24\text{ (two decimal places)} \end{gathered}`

Hence, the test statistics, t = -3.24 ( two decimal places)