In Las Vegas, Nevada, and Atlantic City, New Jersey, tests are performed often on the various gaming devices used in casinos. For example, dice are often tested to determine if they are balanced. Suppose you are assigned the task of testing a die, using a two-tailed test to make sure that the probability of a 2-spot is 1/6. Using the 5% significance level, determine how many 2-spots you would have to obtain to reject the null hypothesis when your sample size is
a. 120
b. 1200
c. 12,000
Calculate the value of for each of these three cases. What can you say about the relationship between (1) the difference between and 1/6 that is necessary to reject the null hypothesis and (2) the sample size as it gets larger?