Question

3. A survey of 41 emergency room patients found that the average waiting time for treatment was 150 minutes with a standard deviation of s = 45 minutes.

Find the 95% confidence interval of the population mean of wait times in the emergency room.

We can be 95% confident that the mean waiting time for the emergency room is between ___________ and __________ minutes.

Answer 1

olution :

Given that,

= 150

s = 45

n = 41

Degrees of freedom = df = n - 1 = 41- 1 = 40

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,40 =2.021

Margin of error = E = t_/2,df * (s /n)

= 2.021 * (45 / 41) = 14.2032

The 95% confidence interval estimate of the population mean is,

- E < < + E

150- 14.2032 < < 150 + 14.2032

135.7968 < < 164.2032

(135.7968 to 164.2032 )