Question

REALLY need help with this!

when a fair coin is flipped, we all know that the probability the coin lands on heads is 0.50. however, what if a coin is spun? according to an article, 2 polish math professors and their students spun a Belgian euro coin 250 times. it landed heads 140 times. one of the professors concluded that the coin was minted asymmetrically. a representative from the Belgian mint said the result was just chance.
(a) state the hypotheses we are interested in testing

Answer 1

The null hypothesis is that the result was just chance.
The alternative hypothesis is that the result wasn't just chance, but rather that the coin was minted asymmetrically.

Answer 2

yes I understand that but I'm unsure about the alternate hypothesis. the null would be \[H_{O}= \mu= 0.50\] correct?

Answer 3

You could phrase it like that. However, I like phrasing the null and alternative hypotheses in terms of words and not numbers. The reason is because we do stats for a purpose (other than when we're made to do it), and nobody cares that your conclusion is going to be "The myu is 0.50". It's not relatable. Rather, they'll care that you've concluded that the coin was not a fair one. Of course, I'll use the myu when I convert the number to a Z-Value to test whether there is enough evidence for us to reject the null hypothesis. I must say, I suppose it also depends on your teacher - if she's asking you to phrase it in that way, then go for it, but I think it's important to understand that they're the same thing.

Answer 4

that's the way he taught the whole unit

Answer 5

it depends on the initial tilting of a coin. You can't always place it vertically when spinning. Especially 250 times. It will tilt. If it lands on heads, that means the bottom is tails. That means when the coin is tilted, the tail is at the bottom. Its center of gravity is at tails. Thus, it will land on heads.

Answer 6

If your null is P = 0.5, your alternative will be that P doesn't equal 0.5.

You would determine your confidence interval, obtain the Z value, find out the probability of the Z value, determine if it's in the critical region and then accept/reject the null hypothesis

Answer 7

(b) show that the conditions for performing a one sample z-test for a proportion are satisfied