It means that the data is more self centered to a certain side.
Answer:
a) 0.3495
b) (9.65, 10.35)
Step-by-step explanation:
We are given the following in the question:
Sample mean,
= 10 hours
Sample size, n = 64
Alpha, α = 0.02
Population standard deviation, σ = 1.2 hours
a) Margin of error
Formula
![z_{critical}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Putting values, we get,
![M.E = (2.33)\dfrac{1.2}{\sqrt{64}} = 0.3495](https://tex.z-dn.net/?f=M.E%20%3D%20%282.33%29%5Cdfrac%7B1.2%7D%7B%5Csqrt%7B64%7D%7D%20%3D%200.3495)
b) the sample mean is 10 hours, then the 98% confidence interval
![\bar{x} \pm M.E](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%5Cpm%20M.E)
Putting the values, we get,
![10\pm 0.3495\\=(9.6505, 10.3495)\\\approx (9.65, 10.35)](https://tex.z-dn.net/?f=10%5Cpm%200.3495%5C%5C%3D%289.6505%2C%2010.3495%29%5C%5C%5Capprox%20%289.65%2C%2010.35%29)
Three points are collinear if their determinant is equal to 0
So,
| 0 -10 1 |
| -3 -15 1 |
| 2 -6 1 |
We must put 1 at the third column since we don't have z in these points, and 1 is a neutral factor.
Applying sarrus
( 0 . -15 . 1 + -10 . 1 . 2 + 1 . -3 . -6) - (1 . -15 . 2 + 0 . 1 . -6 + -10 . -3 . 1)
(0 - 20 + 18) - (-30 + 0 + 30)
(-2) - (0)
-2
Our determinant is different than 0, so these points are not collinear.
-7, -1, 2, and 3 are the zeros of the polynomial