Answer:
The confidence interval estimate of the population mean = (4139.28,4545.56)
Step-by-step explanation:
We are given the following data set:
4041, 3894, 3865, 4037, 4316, 4803, 4660, 4027, 5000, 4821, 4334, 4311
Formula:
where
are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 90852.00696 + 201077.507 + 227926.6736 + 93279.3403 + 697.840278 + 212137.0069 + 100859.1736, +99487.67363 + 432415.8402 + 229042.0069 + 70.84027778 + 987.0069447 = 1688832.917
Confidence interval:
Putting the values, we get,
![4342.42 \pm 1.795885(\frac{391.83}{\sqrt{12}} ) = 4342.42 \pm 203.14 = (4139.28,4545.56)](https://tex.z-dn.net/?f=4342.42%20%5Cpm%201.795885%28%5Cfrac%7B391.83%7D%7B%5Csqrt%7B12%7D%7D%20%29%20%3D%204342.42%20%5Cpm%20203.14%20%3D%20%284139.28%2C4545.56%29)