Chapter 9.3, Problem 1.2CYU

To determine

To compute: The P -value and explain the conclusion that could be drawn.

Answer to Problem 1.2CYU

The P -value is 0.221.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left(\overline{x}\right)=17\\ \text{Sample size}\left(n\right)=18\\ \text{Sample standard deviation}\left(s\right)=60\\ \text{Test statistic}\left(t\right)=1.273\end{array}$

Formula used:

The test statistic is computed as:

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

Here,

  $\begin{array}{l}\overline{x}=\text{Sample mean}\\ \mu \text{= Population mean}\\ n=\text{}\text{Sample size}\\ s=\text{ Sample standard deviation }\end{array}$

Calculation:

The degree of freedom is computed as:

  $\begin{array}{c}Df=n-1\\ =18-1\\ =17\end{array}$

The P -value can be calculated as:

  $\begin{array}{c}P-value=2\times P\left(t>|1.2\right)\\ =0.221\end{array}$

Here, P -value (0.221) is greater than the significance level (0.05). The decision is to reject the null hypothesis.