Question

A college statistics professor has office hours from 9am to 10:30am daily. A sample of waiting time to see the professor(in minutes) is 10,12 20, 15, 17, 10, 30, 28,35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23. Assuming standard deviation is 7.84, find the 95.44% confidence interval for the population mean.
a) -7.7 to 7.8 minutes
b) 19.5 to 35.1 minutes
c) -3.5 to 3.5 minutes
d) 18.8 to 25.8 minutes

Answer 1

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:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{446}{20} = 22.3$

Confidence interval:

$\bar{x} \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.0456} = \pm 2.00$

$22.3 \pm 2.00(\frac{7.84}{\sqrt{20}} ) = 22.3 \pm 3.50 = (18.8,25.8)$

The confidence interval is (18.8,25.8).