A. -10.30 to -4.23
CI = (d bar) ± tα/₂ • (sd/√n)
1) Find di
-11, -5.5, -9.4, -13.6, 2.9, -10.7, 0.1, -7.4, -21.5, 5.3, 3.8, -11.4, -13.4, -13.1, -9, -3.9, -5.7
∑di = -123.5
2) Find (d bar)
(d bar) = ∑di/n = -123.5/17 = -7.264705882
3) Find [di - (d bar)]²
13.9524, 3.11419, 4.55948, 40.13595, 103.32125, 11.80125, 54.23889, 0.018304, 202.64360, 157.87183, 122.42772, 17.10066, 37.64183, 34.05066, 3.011246
4) Find sd
sd = √{∑[di - (d
bar)]²/(n-1)}
sd = √(819.658815/16) = 7.157421018
5) Find df; df=n-1 = 17-1 = 16
6) Find tα/₂
CL=1-α
0.9=1-α
α=0.10; α/2=0.05
t₀.₀₅ w/ 16 df = ±1.746
7) Plug it all in
CI: (d bar) ± tα/₂ • sd/√n
= -7.264705882 ±1.746 • 7.157421018/√17
B.
a. We can be 90% confident that the weight gain that'd be obtained, on average, by using the family therapy treatment is somewhere between the endpoints of the confidence interval.
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