Solution-A:
xbar=47.86
s=19.60
n=20
alpha=0.10
alpha.2=0.10/2=0.05
df=n-1=20-1=19
tcrit in excel
=T.INV(0.05,19)
=1.729132812
90% confidence interval for mean is
xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)
47.86-1.729132812*19.60/sqrt(20),47.86+1.729132812*19.60/sqrt(20)
40.28174,55.43826
(40.28,55.44)
ANSWER(A)
(40.28,55.44)
Solution-b:
margin of error=t*s/sqrt(n)
=1.729132812*19.60/sqrt(20)
=7.578259
ANSWER:
margin of error=7.58
Solution-c:
90% confidence interval for mean is
xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)
47.86-1.729132812*20/sqrt(20),47.86+1.729132812*20/sqrt(20)
40.12708,55.59292
40.13,55.59
ANSWER
(B)the new confidence interval(40.13,55.59) is narrower than interval from part(A)
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