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.

1	2
66	52
61	37
47	57
48	47
68	54
46	53

Find a 95% confidence interval for the mean​ difference, muμ1minus−muμ2​, in ages of houses in the two neighborhoods. (__,__)

​(Round to two decimal places as​ needed.)

​b) Is 0 within the confidence​ interval?

Yes

No

​c) What does the confidence interval suggest about the null hypothesis that the mean difference is​ 0?

A.

Fail to rejectFail to reject

Upper H 0H0

since 0

isis

a plausible value for the true mean difference.

B.

RejectReject

Upper H 0H0

since 0

isis

a plausible value for the true mean difference.

C.

Fail to rejectFail to reject

Upper H 0H0

since 0

is notis not

a plausible value for the true mean difference.

D.

RejectReject Upper H 0H0 since 0 is not a plausible value for the true mean difference.

Answer 1

	Neighborhood 1	Neighborhood 2
sample mean x =	56.00	50.00
standard deviation s=	10.139	7.155
sample size n=	6	6

Pooled Std dev Sp=√((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			8.77
Point estimate : x1-x2=		6.0000
std. error se =Sp*√(1/n1+1/n2)=		5.0662

point estimate of difference=x1-x2=		6.000
for 95 % CI & 10 df value of t=		2.228	from excel: t.inv(0.975,10)
margin of error E=t*std error =		11.2876
lower bound=mean difference-E=		-5.29
Upper bound=mean differnce +E=		17.29
from above 95% confidence interval for population mean =(-5.29 , 17.29)

b)

Yes

c)

A) Fail to reject Ho since 0 is a plausible value for the true mean difference.