You have been doing research for your statistics class on the prevalence of binge drinking among teens.
a. According to 2011 Monitoring the Future data, the average binge drinking score, for this
sample of 914 teens, is 1.27, with a standard deviation of 0.80. Binge drinking is defined as the
number of times the teen drank five or more alcoholic drinks during the past week. Construct
the 95% confidence interval for the true average severe binge drinking score. The confidence
interval is:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)