Spring 2017 Zachary Bradshaw 513 17 10:32 A Test: Final Exam Time Remaining: 01:
ID: 3231329 • Letter: S
Question
Spring 2017 Zachary Bradshaw 513 17 10:32 A Test: Final Exam Time Remaining: 01:58:43 Submit T This Question: 8 pts 2 of 21 (0 complete) This Test: 117 pts poss IE Question Help A developer collects a random sample of the ages of houses from two neighborhoods and finds that the summary statistics for each are as shown, Assume that the data come from a Neighborhood 1 Neighborhood 2 distribution that is Normally distributed. Complete parts a through d below. n1340 1 57.2 2 44.2 7.02 S2 737 a) Find a 95% confidence interval for the mean difference, u2, in ages of houses in the two neighborhoods if df 60.9. (Round to two decimal places as needed.) hy is the confidence interval found in part a narrower than this one? O A. The sample sizes are larger O B. The critical value of the confidence interval is larger for the original confidence interval. O C. The sample means are significantly larger when there are more data values. c) ls 0 within the confidence interval found in part a? Click to select your answer(s). searchExplanation / Answer
a)
Standard error SE (y1-y2) = sqrt (S12 /n1 + S22 /n2)
=sqrt(7.022/40 + 7.372/30)
=sqrt(1.2320 +1.8106)
=sqrt(3.0426)
=1.7443
95% confidence interval for the mean difference
df =60.
=1-0.95
/2 =0.025
t value =t 0.025,df=60 =2.0000
confidence interval C.I =(y1-y2) ± t /2 . SE (y1-y2)
= (57.2-44.2) ± 2.0 (1.7443)
=13 ± 3.4886
=(9.5114 ,16.4886)
b) because the sample sizes are larger the confidence interval is narrower than we calculated neighbourhood houses. but the sample sizes are 40 and 30 . so it is narrower.
c) No, calculated CI is (9.5114 ,16.4886), but 0 is not with in the CI
d)confidence interval doesnot contain the value 0, it suggest reject our Ho
option D is correct
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