Question

A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample​ (in years). Assume that the data come from a distribution that is Normally distributed. Complete parts a through c below.

Neighborhood 1 (58,52,63,66,51,46)

Neighborhood 2 (37,34,33,44,51,53)

a) Find a 95​% confidence interval for the mean​ difference, μ1−μ2​, in ages of houses in the two neighborhoods.

= ( , )

Answer 1

A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample​ (in years). Assume that the data come from a distribution that is Normally distributed. Complete parts a through c below.

Neighborhood 1 (58,52,63,66,51,46)

Neighborhood 2 (37,34,33,44,51,53)

a) Find a 95​% confidence interval for the mean​ difference, μ1−μ2​, in ages of houses in the two neighborhoods.

= (3.4702, 24.5298)

Population 1 Sample
Sample Size	6
Sample Mean	56
Sample Standard Deviation	7.6681
Population 2 Sample
Sample Size	6
Sample Mean	42
Sample Standard Deviation	8.6718
Intermediate Calculations
Population 1 Sample Degrees of Freedom	5
Population 2 Sample Degrees of Freedom	5
Total Degrees of Freedom	10
Pooled Variance	67.0000
Standard Error	4.7258
Difference in Sample Means	14.0000

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	95%
Intermediate Calculations
Degrees of Freedom	10
t Value	2.2281
Interval Half Width	10.5298
Confidence Interval
Interval Lower Limit	3.4702
Interval Upper Limit	24.5298