Question

Suppose a group is interested in determining whether teenagers obtain their driver's licenses at approximately the same average age across the country. Suppose that the following data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their driver's licenses

$\begin{array}{|llllll|}\hline & \text{Northeast}& \text{South}& \text{West}& \text{Central}& \text{East}\\ & 16.3& 16.9& 16.4& 16.2& 17.1\\ & 16.1& 16.5& 16.5& 16.6& 17.2\\ & 16.4& 16.4& 16.6& 16.5& 16.6\\ & 16.5& 16.2& 16.1& 16.4& 16.8\\ \overline{x}=& & & & & \\ s^2=& & & & & \\ \hline\end{array}$

$\alpha =0.01$

a) Decision = _____

b) Conclusion = _____

Short answer

We accept the null hypothesis, no difference between regions.

Step-by-step solution

Given Information

The following data are randomly collected from five teenagers in each region of the country.

$\begin{array}{|llllll|}\hline & \text{Northeast}& \text{South}& \text{West}& \text{Central}& \text{East}\\ & 16.3& 16.9& 16.4& 16.2& 17.1\\ & 16.1& 16.5& 16.5& 16.6& 17.2\\ & 16.4& 16.4& 16.6& 16.5& 16.6\\ & 16.5& 16.2& 16.1& 16.4& 16.8\\ \overline{x}=& & & & & \\ s^2=& & & & & \\ \hline\end{array}$

Explanation

Probability Statement: $p$-value $=0.017$

Compare $\alpha$and the $p$-value: $\alpha =0.01,p-value=0.017$

Make a decision: Since $\alpha <p-value$, we accept $H_0$.

Final Answer

We can conclude that the null hypothesis of no difference between the means of five regions is the same will be accepted, at $1\%$level of significance.