Respuesta :
Answer:
95% Confidence interval: Â (12.93, 13.87) Â Â Â
Step-by-step explanation:
We are given the following in the question:
13.03, 14.98, 13.12, 13.13, 13.11, 13.03, 13.16, 14.98, 13.06, 13.05, 13.12, 13.13
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex] Â
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations. Â
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{160.9}{12} = 13.4[/tex]
Sum of squares of differences = 5.94
[tex]S.D = \sqrt{\dfrac{5.94}{11}} = 0.74[/tex]
95% Confidence interval: Â
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex] Â
Putting the values, we get, Â
[tex]t_{critical}\text{ at degree of freedom 11 and}~\alpha_{0.05} = \pm 2.201[/tex] Â
[tex]13.4 \pm 2.201(\dfrac{0.74}{\sqrt{12}} )\\\\ = 13.4 \pm 0.4701 = (12.9299 ,13.8701)\\\approx (12.93, 13.87)[/tex] Â
