91影视

$$\begin{gathered} {\stackrel{炉}{x}}_1=20.3 \\ {\stackrel{炉}{x}}_2=19.2 \\ {n}_1=40 \\ {n}_2=40 \\ {s}_1=2.1 \\ {s}_2=1.9 \\ 伪=0.01 \end{gathered}$$

There are three requirements that must be met:

Random: It is satisfying because the samples were chosen at random from different populations.

Independent: It is satisfying because the sample of $40$grey Eastern grey squirrels represents less than $10\%$of the total grey Eastern grey squirrel population, and the sample of 40 black Eastern grey squirrels represents less than $10\%$of the total black Eastern grey squirrel population.

Normal: It is satisfying because both samples are large, with a sample size of at least $30$for each.

As a result, all of the requirements have been met.

Now, the degree of freedom will be:

$$\begin{gathered} df=min(n_1-1,n_2-1) \\ =min(56-1,56-1) \\ =55 \end{gathered}$$

Then the $t$-value will be as:

$t_{伪/2}=2.750$

As a result, the confidence interval will be:

$$\begin{gathered} ({\stackrel{炉}{x}}_1-{\stackrel{炉}{x}}_2)-t_{\frac{伪}{2}}脳\sqrt{\frac{{s_1}^2}{n_1}+\frac{{s_2}^2}{n_2}} \\ =(20.3-19.2)-2.750脳\sqrt{\frac{2.1^2}{40}+\frac{1.9^2}{40}} \\ =-0.1471 \end{gathered}$$

Therefore, we conclude that we are $99\%$confident that the mean weight of all gray Eastern gray squirrels is between $0.1471$ounces lower and $2.3471$ounces higher than the mean weight of all black Eastern gray squirrels in the forest.

Because the confidence interval gives us a range of possible values for the difference between the true means, whereas the significance test only checks one possible value for the difference between the means, that is, if the means are equal, the confidence interval gives us more information than the significance test.