7. We are interested if humans are capable of generating random numbers. We ask a large number of individuals to pick a random integer between 0 and 9. As there are 10 categories, the degrees of freedom are 9 for the ? 2 test we would run on the data. It turns out that ?2 =d.f., i.e. if the null is true, we'd expect to get a value around 9 here. a. Roughly sketch what the ? 2 distribution with 9 degrees of freedom must look like and mark the rejection region on the graph.

?b. Suppose that the null isn't true (in fact it isn't, people much prefer 7 to 0 or 1 for instance). Suppose that our sample size is sufficient so that the power is .75. Draw what the sampling distribution of our ? 2 statistic must look like in this case (relative to the picture above).

7. We are interested if humans are capable of generating random numbers. We ask a large number of individuals to pick a random integer between I] and Q. As there are 10 categories, the degrees of freedom are 9 for the x2 test we would run on the data. It turns out that pxa =d.f.I i.e. if the null is true, we'd expect to get a value around 9 here. a. Roughly sketch what the )8 distribution with 9 degrees of freedom must look like and mark the rejection region on the graph. b. Suppose that the null isn't true (in fact it isn't, people much prefer T to 0 or 1 for instance). Suppose that our sample size is sufcient so that the power is .75. Draw what the sampling distribution of our x2 statistic must look like in this case (relative to the picture above)