Question

A random sample of 180 residents of Milpitas, CA, was surveyed, and a 95% confidence interval was constructed in order to estimate the average amount of time it takes for residents of Milpitas to commute to work each day. The interval ended up being from 10.25 minutes to 65.74 minutes. What would be a correct interpretation of this interval?  

A. We are 95% confident that if we randomly select one individual from Milpitas, that person will take between 10.25 minutes and 65.74 minutes to commute to work each day

B. We are confident that 95% of the population of Milpitas takes between 10.25 minutes and 65.74 minutes to commute to work each day.

C. We are 95% confident the average commute time for the sample of 180 Milpitas residents is between 10.25 minutes and 65.74 minutes.

D. We are 95% confident the average commute time for all residents of Milpitas is between 10.25 minutes and 65.74 minutes.

E. If we take many samples of size n = 180 from the population of Milpitas residents, 95% of the resulting sample means would fall between 10.25 minutes and 65.74 minutes.

Answer 1

A random sample of 180 residents of Milpitas, CA, was surveyed.

A 95% confidence interval was found to estimate the average time it takea for residents to commute to work.

The interval was 10.25 minutes to 65.74 minutes.

Now, we know that this confidence interval is used to estimate the population average time of commute to work; ie. For all people of Milpitas.

Now, a 95% confidence interval actually denotes a range, which will include the true population average time of commute to work, 95% of the times, if large number of different samples are randomly selected from the population.

So, the correct interpretation of the confidence interval is

option (D) We are 95% confident that the average commute time for all residents of Milpitas is between 10.25 minutes and 65.74 minutes.