A casino must demonstrate to the state gaming commission that every die it uses is fair. a machine is used to roll each die 1200 times. a die is discarded if the following assumption it is fair is rejected at the 10% significance level. determine if the following results suggest a die is accepted or rejected by the casino.
then it proceeds to show a picture of a die with the number 1 rolled 190 times, a die with the number 2 rolled 220 times and a die with the number 4 rolled 185 times.
I guess you are supposed to conclude that occurrences of faces 3. 5. and 6 together amounted to $1200 - 595 = 605$, but are given no information on how many times each of these faces appeared.
In that case you can do a chi-squared goodness of fit test with four categories: '1', '2', '4', and '356'. Their observed counts are 190, 220, 185, and 605, and their expected counts are 200, 200, 200, and 600, respectively. Then the chi-squared goodness-of-fit statistic is $Q = 3.67.$ Under the null hypothesis that the die is fair, $Q \stackrel{approx}{\sim} Chisq(df = 3).$
X = c(190, 220, 185, 605)
E = c(200, 200, 200, 600)
Q = sum((X-E)^2/E); Q
## 3.666667
Since you know something about such tests, and hoping that I have cleared up whatever was confusing you about this problem, I suppose you can take it from there to determine whether to judge that the die is unfair. (The problem would have been straightforward if you had been given observed frequencies for all six faces of the die.)
