Spinning heads? 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 the article “Euro Coin Accused of Unfair Flipping” in the New Scientist, two 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 indicated the result was just chance. Assume that the conditions for inference are met.
a. Carry out a chi-square test for goodness of fit to test if heads and tails are equally likely when a euro coin is spun.
b. In Chapter $9$ Exercise $50$ you analyzed these data with a one-sample $z$ test for a proportion. The hypotheses were $H_{0} : p = 0.5$ and $H_{a} : p \neq 0.5$
where $p =$ the true proportion of heads. Calculate the $z$ statistic and P-value for this test. How do these values compare to the values from part (a)?

Question

Accepted Answer

Part (a) When a euro coin is spun, there is no persuasive evidence that heads and tails are not equally likely.

Part (b) When a euro coin is spun, there is no persuasive evidence that heads and tails are not equally likely.

Short Answer