Question

A developer is recording information about houses in two different neighborhoods, including the year in which they were built. She takes a random sample of 30 houses from Neighborhood 1 and a random sample of 35 houses from Neighborhood 2, resulting in the following summary statistics:

y¯1=57.2; s1=9.51

y¯2=47.6; s2=6.15

Use this information to calculate the lower bound of the 90% (un-pooled) confidence interval for the true difference (neighborhood 1 - neighborhood 2) in average age for houses in these neighborhoods. Use technology (such as an online t-distribution calculator) to find the appropriate value of the multipler.

Round your answer to 3 decimal places.

Answer 1

The statistical software output for this problem is:

Two sample T summary confidence interval: P1 : Mean of Population 1 12 : Mean of Population 2 V1 - P2 : Difference between two means (without pooled variances) 90% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit Hi-H2 9.6 2.0236879 48.231061 6.2061416 12.993858

Hence,

Lower bound of 90% confidence interval = 6.206