Let X ~ N(μx, o) and Y ~ N(µy, o?). Suppose we are given the following indepen- dently sampled data for X and Y³: sample for X sample for Y : 24.8 12.8 11.1 11.1 15.9 12.2 18.3 8.9 5.6 12.8 17.3 11.3 : 26.6 26.3 25.2 23.3 22 20.2 26.1 21.1 14.6 14.5 21.8 22.8 21.5 22.3 31 11.5 Compute a 95% confidence interval of μx - μy (i) using the knowledge that o = o} = 4.7; (ii) assuming we do not know the values of ox, oy, but we still know that ox = 0y = 0 for some unknown σ.

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Let X~ N(ux, o) and Y ~ N(μy, o). Suppose we are given the following indepen-
dently sampled data for X and Y³:
sample for X
sample for Y
: 24.8 12.8 11.1 11.1 15.9 12.2 18.3 8.9 5.6 12.8 17.3 11.3
: 26.6
26.3 25.2 23.3 22 20.2 26.1 21.1 14.6 14.5 21.8 22.8
21.5 22.3 31
11.5
Compute a 95% confidence interval of px - μy
(i) using the knowledge that o = o} = 4.7;
(ii) assuming we do not know the values of σx, σy, but we still know that σx = Ốy = 0
for some unknown σ.
Transcribed Image Text:Let X~ N(ux, o) and Y ~ N(μy, o). Suppose we are given the following indepen- dently sampled data for X and Y³: sample for X sample for Y : 24.8 12.8 11.1 11.1 15.9 12.2 18.3 8.9 5.6 12.8 17.3 11.3 : 26.6 26.3 25.2 23.3 22 20.2 26.1 21.1 14.6 14.5 21.8 22.8 21.5 22.3 31 11.5 Compute a 95% confidence interval of px - μy (i) using the knowledge that o = o} = 4.7; (ii) assuming we do not know the values of σx, σy, but we still know that σx = Ốy = 0 for some unknown σ.
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