Respuesta :
Answer:
95% confidence interval: (67.97,84.69)
Step-by-step explanation:
We are given the following data set:
64, 82, 74, 73, 78, 87
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]\bar{x} =\displaystyle\frac{458}{6} = 76.33[/tex]
Sum of squares of differences = 317.33
[tex]s = \sqrt{\dfrac{317.33}{5}} = 7.97[/tex]
95% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 5 and}~\alpha_{0.05} = \pm 2.5705[/tex]
[tex]76.33 \pm 2.5705(\dfrac{7.97}{\sqrt{6}} )\\\\ = 76.33 \pm 8.3637\\\\ = (67.9663 ,84.6937)\approx (67.97,84.69)[/tex]
(67.97,84.69) is the required 95% confidence interval.
