Answer:
Option D) 18.8 to 25.8 minutes
Step-by-step explanation:
We are given the following data set:
10,12,20, 15, 17, 10, 30, 28,35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23
Standard deviation = 7.84
Confidence level = 1 - Significance Level = 1 - 95.44% = 4.56% = 0.0456
Formula:
![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{446}{20} = 22.3](https://tex.z-dn.net/?f=Mean%20%3D%5Cdisplaystyle%5Cfrac%7B446%7D%7B20%7D%20%3D%2022.3)
Confidence interval:
![\bar{x} \pm z_{critical}\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%20%5Cpm%20z_%7Bcritical%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Putting the values, we get,
![z_{critical}\text{ at}~\alpha_{0.0456} = \pm 2.00](https://tex.z-dn.net/?f=z_%7Bcritical%7D%5Ctext%7B%20at%7D~%5Calpha_%7B0.0456%7D%20%3D%20%5Cpm%202.00)
![22.3 \pm 2.00(\frac{7.84}{\sqrt{20}} ) = 22.3 \pm 3.50 = (18.8,25.8)](https://tex.z-dn.net/?f=22.3%20%5Cpm%202.00%28%5Cfrac%7B7.84%7D%7B%5Csqrt%7B20%7D%7D%20%29%20%3D%2022.3%20%5Cpm%203.50%20%3D%20%2818.8%2C25.8%29)
The confidence interval is (18.8,25.8).