Statistics Question

Question

In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n = 20 = 4.33 s = 3.50 Based on this information, the upper limit for a 95 percent confidence interval estimate for the true population mean is: about 7.83 miles. about 5.97 miles. nearly 12.0 miles. about 5.86 miles.

Answer 1

Sara,

 

A population with a normal distribution has 95% of its observations within two standard deviations of the normal distribution.

 

Sample distributions have the same mean as their population distributions, so we can use xbar = 4.33 mi as the mean of both.

 

The standard deviation of a population can be approximated by the standard deviation of a sample s divided by sqrt(n-1), which is 3.50/sqrt(19) = 0.803 mi.

 

Upper limit for 95% confidence = 4.33 + 2*0.803 = 5.94 mi, which is closest to the choice 5.97 mi.

 

Michael.