Suppose we want to test to see if a roulette wheel is balanced. The wheel is spun 100 time resulting in 58 red outcomes. Is this evidence that the roulette wheel is out of balance

Solution :

Here, = sample proportion of red outcomes

= 0.58

So we have to test,

V/S    

The test statistic is

  = 1.600

P value using the z table is 0.110

So P value greater than 0.05

Therefore, there is no evidence that roulette wheel is out of balance.

it would be 6xy and -16xy.