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 onesample z test for a proportion. The hypotheses were H₀: p = 0.5 and H_a: p ≠ 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)?

Exercise 50.

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Type of university Public Private Total 5 or fewer 1951 1028 2979 6 to 10 2688 1285 3973 Distance 11 to 50 10,971 5527 16,498 from home (miles) 51 to 100 6765 2211 8976 101 to 500 15,177 6195 21.372 Over 500 5811 9486 15,297 Total 43,363 25,732 69,095