Question

During a medical emergency, people who dial 911 expect an ambulance to arrive quickly and personnel to provide vital care. A random sample of 40 ambulance response times in minutes were collected. A 95% confidence interval for the population mean response time for ambulances is found to be 7.5 minutes to 9.5 minutes.We estimate, the average distance of the possible sample mean values (for repeated samples of the same size n) from the population mean value to be about ___________ minutes.a. 0.4943b. 2.023c. 3.126

Answer 1

c. 3.126

Explanation:

95% confidence interval for the population mean response time for ambulances is found to be 7.5 minutes to 9.5 minutes

Confidence Intervals can also be formulated as M±ME where

• M is the sample mean
• ME is the Margin of error

M-ME=7.5 and M+ME=9.5 from this we get ME=1

Margin of error (ME) around the mean can also be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the corresponding statistic in the given confidence level(z-score)

• s is the standard deviation of the sample(or of the population if it is known)

• N is the sample size

By replacing the numbers we get:

ME=1=
`(1.96*s)/(√(40) )` solving this equation for s we get

s≈3.126

s can also interpreted as the mean squared distances of samples from the population mean.