There were two kinds of chocolate: Sam's Choice or Cote d'Or; the latter selling for about $2.90 and the former $1.90, each a 3.5 ounce bar of 70% cocoa. Each of n=15 of you provided a preference of chocolate sample 0 or chocolate sample 1 (one person abstained and I dis-regarded that datum). I had randomized which type of chocolate was labeled as '0' or '1', using the code 0=Cote d'Or and 1=Sam's and the random sequence of 0s and 1s given by R being given in the table below.
ID# Random# O-label 1-label Resp Pref 1 1 C S 1 S 2 1 C S 0 C 3 1 C S 0 C 4 1 C S 0 C 5 0 S C 0 S 6 0 S C 1 C 7 0 S C NONE 8 0 S C 1 C 9 1 C S 0 C 10 0 S C 0 S 11 0 S C 1 C 12 1 C S 1 S 13 0 S C 0 S 14 1 C S 1 S 15 0 S C 0 S 16 0 S C 0 SIn class, we chose a value x.star such that P(X >= x.star) is less than or equal to .05, and x.star is as close to 7.5 as possible. By trial and error:
x <- 11:15
y <- 1-pbinom(x-1,15,.5)
cbind(x,round(y,4))
x
[1,] 11 0.0592
[2,] 12 0.0176
[3,] 13 0.0037
[4,] 14 0.0005
[5,] 15 0.0000
Thus x.star = the critical number is 12 and we reject H_0 in favor of H_1 iff X >= 12; this test has an alpha of .0176.
The data above show x=7; so we cannot reject the null.