Question

A study was done to determine the average number of homes that a homeowner owns in his or her lifetime. For the 60 homeowners surveyed, the sample average was 4.2 and the sample standard deviation was 2.1. Calculate the 95% confidence interval for the true average number of homes that a person owns in his or her lifetime.

A) (3.90, 4.50)
B) (3.66, 4.74)
C) (4.01, 4.39)
D) (3.67, 4.73)

Answer 1

D) (3.67, 4.73)

Explanation:

Confidence Interval for the true average number of homes that a person owns in his or her lifetimecan be calculated using M±ME where

• M is the average number of home owned (4.2)

• ME is the margin of error from the mean

And margin of error (ME) can be calculated as

ME=
`(z*s)/(√(N) )` where

• z is the corresponding statistic in the given confidence level(1.96)

• s is the standard deviation of the sample(2.1)

• N is the sample size (60)

Putting the numbers we get ME=
`(1.96*2.1)/(√(60) )`≈0.53

Then the 95% confidence interval is 4.2±0.53 or (3.67, 4.73)