Chapter 9.3, Problem 67E

a.

To determine

To find: The test statistic

Answer to Problem 67E

The test statistic is 2.409

Explanation of Solution

Given:

Sample size (n) = 45

Sample mean $\left(\overline{x}\right)=125.7$

Sample standard deviation ( s ) = 29.8

Formula used:

The test statistic is:

  $t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}$

Calculation:

The test statistic can be calculated as:

  $\begin{array}{c}t=\frac{\overline{x}-\mu }{\frac{s}{\sqrt{n}}}\\ =\frac{125.7-115}{\frac{29.8}{\sqrt{45}}}\\ =2.409\end{array}$

Hence, the value is 2.409.

b.

To determine

To find: The P -value.

Answer to Problem 67E

The P -value is 0.0101.

Explanation of Solution

Degree of freedom is n -1 = 45-1 = 44

The P -value is calculated as:

  $\begin{array}{c}P-value=P\left(t_c>\left|0.77\right|\right)\\ =0.0101\end{array}$

Now, the P -value by using Ti-83 plus is:

  

The P -value is 0.0101.