Question

Professor Chang has recently taken a psychic course and claims to have the ability to predict the outcome of a coin flip. To prove this claim, Chang attempted to ”foresee” the outcome before a coin was flipped. The results were 5 successes out of 6 attempts. He states that is ”good enough” evidence to prove his psychic training was worth it.
1. As an aspiring statistics student you would like to show at a 15% significance level, whether or not Mr. Chang has increased his ability to correctly choose the outcome of a coin flip.

(a) Present the appropriate null and alternative hypotheses for such a test.

(b) Assess normality (significantly large), and explain significance of your results.

(c) What is the probability of observing the singular outcome as described in the problem? What is the p-value of our test?

(d) Conclude in context.

Answer 1

(a) Present the appropriate null and alternative hypotheses for such a test.

The hypothesis being tested is:

H0: p = 0.5

Ha: p > 0.5

(b) Assess normality (significantly large), and explain significance of your results.

The test statistic, z = (p̂ - p)/√p(1-p)/n = (0.83 - 0.5)/√0.5(1-0.5)/6 = 1.63

(c) What is the probability of observing the singular outcome as described in the problem? What is the p-value of our test?

The p-value is 0.0512.

(d) Conclude in context.

Since the p-value (0.0512) is less than the significance level (0.15), we can reject the null hypothesis.

Therefore, we can conclude that Mr. Chang has increased his ability to correctly choose the outcome of a coin flip.

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