All euros have a national image on the \"heads\" side and a common design on the
ID: 3022182 • Letter: A
Question
All euros have a national image on the "heads" side and a common design on the "tails" side. Spinning a coin, unlike tossing it, may not give heads and tails with equal probabilities. Polish students spun the Belgian euro 260 times, with its portly king, Albert, displayed on the heads side. The result was 150 heads. How significant is this evidence against equal probabilities? Follow the four-step process. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = Conclusion: There is convincing evidence that the proportion of times a Belgian Euro coin spins heads is not 0.50. There is no evidence to conclude that the proportion of times a Belgian Euro coin spins heads is not 0.50. There is moderately suggestive evidence to conclude that the proportion of times a Belgian Euro coin spins heads is not 0.50. There is suggestive, but inconclusive evidence to conclude that the proportion of times a Belgian Euro coin spins heads is not 0.50. You may need to use the appropriate Appendix Table to answer this question.Explanation / Answer
Formulating the null and alternatuve hypotheses,
Ho: p = 0.5
Ha: p =/= 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.576923077
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.031008684
Getting the z statistic,
z = (p^ - po)/sp = 2.480694692 [ANSWER, Z VALUE]
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As this is a 2 tailed test, then, getting the p value,
p = 0.013112663 [ANSWER, P VALUE]
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As this is a small P value < 0.05, then
OPTION A: There is convincing evidence that the proportion of times a belgian euro coin spins is not 0.50. [ANSWER, A]
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