Answer:
99% Confidence interval: (183,246)
Step-by-step explanation:
We are given the following data set:
141, 144, 150, 161, 169, 179, 186, 194, 199, 209, 219, 220, 226, 237, 254, 261, 275, 278, 286, 295
Formula:
where
are data points,
is the mean and n is the number of observations.
![Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cdisplaystyle%5Cfrac%7B%5Ctext%7BSum%20of%20all%20observations%7D%7D%7B%5Ctext%7BTotal%20number%20of%20observation%7D%7D)
![Mean =\displaystyle\frac{4283}{20} = 214.15](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B4283%7D%7B20%7D%20%3D%20214.15)
Sum of squares of differences = 45922.55
![S.D = \sqrt{\frac{45922.55}{19}} = 49.16](https://tex.z-dn.net/?f=S.D%20%3D%20%5Csqrt%7B%5Cfrac%7B45922.55%7D%7B19%7D%7D%20%3D%2049.16)
99% Confidence interval:
Putting the values, we get,