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:
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{446}{20} = 22.3[/tex]
Confidence interval:
[tex]\bar{x} \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.0456} = \pm 2.00[/tex]
[tex]22.3 \pm 2.00(\frac{7.84}{\sqrt{20}} ) = 22.3 \pm 3.50 = (18.8,25.8)[/tex]
The confidence interval is (18.8,25.8).
