Question

An important factor in selling a residential property is the number of people who look through the home. A sample of 11 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 17 and the standard deviation of the sample was 3 people. Develop a 90% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

Can someone help with this... I thought it was 15.5 : 18.5 however it is saying that is incorrect.

Answer 1

Given

Sample size=n=11

Degree of freedom=df=n-1=11-1=10

Sample mean==17

Sample standard deviation=s=3

Since population standard deviation is not given, we approximate it with sample standard deviation.

So,

=s=3

Standard error of mean of infinite population is given as

Refer to t-distribution table for 10 degrees of freedom and 90% confidence level, we get

t=1.812

Lower bound of confidence interval=-t*=17-1.812*0.904534=15.36098 or 15.36

Upper bound of confidence interval=+t*=17+1.812*0.904534=18.63902 or 18.64