Chapter 10, Problem 10CRE

To determine

To Write: the few sentences summarizing the comparison of males and female.

Answer to Problem 10CRE

There is not enough proof to reject the claim that the population mean is equal for men and women.

Explanation of Solution

Given:

  

  $\begin{array}{c}{\overline{x}}_1=55.516\\ {\overline{x}}_2=57.915\\ s_1=12.696\\ s_2=12.265\\ n_1=31\\ n_2=47\end{array}$

Formula used:

  $t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_1}}}$

Calculation:

The hypotheses:

  $\begin{array}{c}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1\ne {\mu }_2\end{array}$

The test statistic:

  $\begin{array}{c}t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_1}}}\\ =\frac{55.516-57.915}{\sqrt{\frac{{12.696}^2}{31}}+\frac{{12.265}^2}{47}}\\ =-0.8276\end{array}$

Degrees of freedom:

  $df=62.8$

The P-value is the probability of getting the value of the test statistic, or a value more extreme.

  $P=0.4110$

If the P-value is equal or les than to the significance level, then the null hypothesis is rejected:

  $P>0.05\Rightarrow \text{Fail to reject }{H}_0$

There is not enough proof to reject the claim that the population mean is equal for men and women.