After losing all your money at the roulette wheel. You want to prove that the wheel is rigged. On a standard roulette wheel, red numbers will turn up 18 out of 38 times. In other words, in the long run, the proportion of red numbers will be 0.47. After betting on the roulette wheel 400 times, you record 196 red numbers. Can you prove that the roulette wheel is rigged to land on red numbers at a different proportion than expected

To test if the null hypothesis, in this case the wheel being rigged, we need to perform a number of tests and find the p value. If the p value is above a certain level, then it is statistically significant and we can say that the null hypothesis is correct.

It is stated that the standard rate of getting a red number is 0.47, which is 47%. Out of 400, to get a 47% rate, we would need to have red 188 times which is less than 196 so the test results in a rate above 47% in which case the null hypothesis is correct and we can say that the wheel is rigged.

I hope this answer helps.