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.
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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 
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