A developer wants to know if the houses in two different neighborhoods were buil

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 Click the icon to view the data table a) Find a 95% confidence interval for the mean difference. 1-2, in ages of houses in the two neighborhoods. i Data Table Round to two decimal places as needed.) b) Is 0 within the confidence interval? O Yes Neighborhood 1 59 65 63 52 57 46 Neighborhood 2 45 O No c) What does the confidence interval suggest about the null hypothesis that the mean difference is 0? O A. Fail to reject Ho since 0 is not a plausible value for the true mean difference 52 42 43 B. ( C. 0 D. Reject H0 since 0 is a plausible value for the true mean difference Fail to reject Ho since 0 is a plausible value for the true mean difference Reject Ho since 0 is not a plausible value for the true mean difference Print Done

Explanation / Answer

X1bar= 57 , S1= 7.07 x2bar= 44, S2= 6.57

95% confidence interval

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((7.07)^2/6) + (6.57)^2/6)) = sqrt (49.98/6+ 43.16/6)= sqrt (8.33+7.19)= sqrt(15.52)= 3.94

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 13 ± (2.23 * 3.94) = 13 ± 8.79

1 - 2 = (M1 - M2) = 13, 95% CI [4.21,21.79].

You can be 95% confident that the difference between your two population means (1 - 2) lies between 4.21 and 21.79

b) No, zero is not within the confidence interval.

c) Reject H0, since 0 is NOT a plausible value for the true mean difference.

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