Question

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

Answer 1

Here,
`$ \hat p$` = sample proportion of red outcomes

`$ \hat p =(58)/(100)$`

`$ \hat p$` = 0.58

So we have to test,

`$H_0 : p = 0.5$`

V/S
`$H_a: p \\eq 0.5 $`

The test statistic is

`$z = \frac{\hat p - p}{\sqrt{(p(1-p))/(n)}}$`

`$z = \frac{0.58 - 0.5}{\sqrt{(0.5(1-0.5))/(100)}}$`

`$=(0.08)/(0.05)$`

= 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.