> library(Sleuth3)
> summary(case0101)
     Score           Treatment
 Min.   : 5.00   Extrinsic:23 
 1st Qu.:14.90   Intrinsic:24 
 Median :18.70                
 Mean   :17.86                
 3rd Qu.:21.25                
 Max.   :29.70                

> t.test(case0101$Score ~ case0101$Treatment)

        Welch Two Sample t-test

data:  case0101$Score by case0101$Treatment
t = -2.9153, df = 43.108, p-value = 0.005618
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -7.010803 -1.277603
sample estimates:
mean in group Extrinsic mean in group Intrinsic
               15.73913                19.88333

> t.test(case0101$Score ~ case0101$Treatment,alternative="less")

        Welch Two Sample t-test

data:  case0101$Score by case0101$Treatment
t = -2.9153, df = 43.108, p-value = 0.002809
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
      -Inf -1.754626
sample estimates:
mean in group Extrinsic mean in group Intrinsic
               15.73913                19.88333

> 18.48+c(-1,1)*1.96*2.9/sqrt(20)
[1] 17.20902 19.75098
> 18.48+c(-1,1)*qnorm(.975)*2.9/sqrt(20)
[1] 17.20904 19.75096
> 18.48+c(-10,9,2,11)*qnorm(.975)*2.9/sqrt(20)
[1]  5.770423 29.918619 21.021915 32.460535
> 22.5 + c(-1,1)*qt(.995,7)*7.19/sqrt(8)
[1] 13.60414 31.39586
> qt(.995,7)
[1] 3.499483
> qnorm(.995)
[1] 2.575829
> 22.5 + c(-1,1)*qt(.995,99)*7.19/sqrt(8)
[1] 15.82355 29.17645
> qt(.995,99)
[1] 2.626405
>