91影视

$H_0:$There is no statistically significant difference in the average number of swims needed by the male and female pups to complete three main escapes.

$Ho:\left({渭}_1-{渭}_2\right)=0$

$H_{伪}:$ The average amount of swims needed by the male and female paps to complete three effective escapes differs significantly.

Under $H_0$test statistics:

$$\begin{gathered} t=\frac{\left({\stackrel{炉}{x}}_1-{\stackrel{炉}{x}}_2\right)}{\sqrt{{\left(\frac{S_1}{n_1}\right)}^2+{\left(\frac{S_2}{n_2}\right)}^2}} \\ =\frac{\left(5.8947-5.5263\right)}{{\left(\frac{\sqrt{2.378}}{19}\right)}^2+{\left(\frac{\sqrt{2.4578}}{19}\right)}^2} \end{gathered}$$

$$\begin{gathered} =\frac{0.3684}{\sqrt{{\left(0.125\right)}^2+{\left(0.129\right)}^2}} \\ =\frac{0.3684}{\sqrt{0.015625+0.016641}} \\ =\frac{0.3684}{0.032266} \\ =0.4696 \end{gathered}$$

Rejection regions are$t>t_{伪/2}\text{or}t<-t_{伪/2}$ where the tale is dependent on $\left(n_d-1\right)$degrees of freedom. Degrees of freedom at a level of 0.10.

Because our test statistic is in the acceptance range, one cannot reject the null hypothesis and may infer that there is a 10% difference in the mean number of Swims necessary to complete four successful escapes by male or female pups.

Conditions required for valid small sample inferences about$\left({渭}_1-{渭}_2\right)$

1. The two samples are drawn at random from the two target populations in an independent way.
2. The distributions of the sampled groups are roughly normal.
3. The variations in the population are equivalent.