Question

# A developer wants to know if the houses in two different neighborhoods were built at roughly...

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.

= ( , )

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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