Respuesta :
We will have the following:
*First: We determine the standard deviation of the statistic, this is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{133}_1(x_i-\mu)^2}{N}}[/tex]So, we will have:
[tex]\mu=\frac{\sum^{133}_1x_i}{N}\Rightarrow\mu=\frac{8911}{133}\Rightarrow\mu=67[/tex]Then:
[tex]\sigma=\sqrt[]{\frac{\sum^{133}_1(x_i-67)^2}{133}}\Rightarrow\sigma=\sqrt[]{\frac{196042}{133}}\Rightarrow\sigma=\sqrt[]{1474}\Rightarrow\sigma=38.39270764\ldots[/tex]And so, we obtain the standar deviation.
*Second: We determine the margin of error:
[tex]me=cv\cdot\sigma[/tex]Here me represents the margin of error, cv represents the critical value and this is multiplied by the standard deviation. We know that the critica value for a 90% confidence interval is of 1.645, so:
[tex]me=1.645\cdot38.39270764\ldots\Rightarrow me=63.15600407\ldots\Rightarrow me\approx63.156[/tex]*Third: We determine the confidence interval as follows:
[tex]ci=ss\pm me[/tex]Here ci is the confidence interval, ss is the saple statistic and me is the margin of error:
[tex]ci\approx133\pm63.156\Rightarrow ci\approx(69.844,196.256)[/tex]And that is the confidence interval,
