9. Grip and Leg Strength. In the paper, "Sex Differences in Static Strength and Fatigability in Three Different Muscle Groups "(Re- search Quarterly for Erercise and Sport, Vol. 61(3), pp. 238-242), J. Misner et al. published results of a study on grip and leg strength of males and females. The following data, in newtons, is based on their measurements of right-leg strength.

Preliminary data analyses indicate that you can reasonably presume leg strength is normally distributed for both males and females and that the standard deviations of leg strength are approximately equal. At the 5% significance level, do the data provide sufficient evidence to conclude that mean right-leg strength of males exceeds that of females? (Note: $\overline{x_1}=$2127, $s_1=$513, =1843, $\overline{x_2}$and $s_2$=446

For the given data sets of males and females we are given the following information.

Males:

${\overline{x}}_1=2127$

$s_1=513$

Females:

${\overline{x}}_2=1843$

$s_2=446$

From the given data sets we can easily identify the sample sizes of two samples as follows.

$n_1=13$

$n_2=14$

$\text{The significance level is}5\%\text{.}$

Here we need to compare two independent small samples for the difference of the means. So we have to consider the student t-test.

Let ${\mu }_1$and ${\mu }_2$denote, respectively the mean right leg strength of males exceeds that of females. To perform the hypothesis test the null and alternative hypothesis are as follows.

$H_0:{\mu }_1={\mu }_2\text{(Mean right leg strength of males not exceeds that of females)}$

$H_a:{\mu }_1>{\mu }_2\text{(Mean right leg strength of males exceeds that of females)}$

Use MINITAB software to perform the t-test as follows.

1) Choose Stat > basic Statistics>2-sample t..

2) Select samples in different columns.

3) Click in first text box and click specifyMales.

4) Click in second text box and click specifyFemales.

5) Uncheck the Assume equal variances check box

6) Click theOptions.... Button

7) Click in the Confidence level text box and type95

8) Click in the test differencetext box and type 0

9) Click arrow button at the right of the Alternativedrop-down list box and select greater than

10) Click Oktwice

The following is the Minitab out put for the hypothesis test.

From the above out put, the P-value for the hypothesis test is 0.068 Because the P-value is greater than the specified significance level of 0.05, we fail to reject$H_0$

Conclusion:

Therefore, the data do not provide sufficient evidence to conclude that the mean right -leg strength of males exceeds that of female.