Question

A person spinning a 1962 penny gets 10 heads out of 50 spins. Because she gets a p-value of 0.00002, she says she has proved the coin is biased. What is the flaw in the statement and how should it be corrected?Choose the correct answer below.A.The flaw is that the spinner said she proved the coin is biased. Hypothesis tests are not used to prove ideas.B.The flaw is that the spinner spun the penny. Flipping the penny would provide a more accurate test.C.The flaw is that the spinner only spun the coin 50 times. She must spin it many more times than that to prove the coin is biased.D.The flaw is that the spinner did not include a significance level. A significance level must be included to know if the null hypothesis can be rejected.E. The flaw is that the spinner used a penny from 1962. A penny from a more recent year would provide a more accurate test.F.The flaw is that the spinner concluded the coin is biased. A very low? p-value proves that the coin is unbiased

Answer 1

D.The flaw is that the spinner did not include a significance level. A significance level must be included to know if the null hypothesis can be rejected.

Explanation:

In hypotheses testing, null and alternative hypotheses are set. In this example

Let p1 be the probability of getting heads out of a spin and

p2 be the probability of getting tails out of a spin

`H_(0) :` p1=p2, that is coin is not biased

`H_(a) :` p1≠p2, that is coin is biased.

To test these hypotheses, sample result observed and p-value of the result express the probability of the sample result occurring under the assumption that null hypothesis is true.

To conclude that the p-value is significant, a significance level has to be set. If the p-value is under the significance level, then null hypothesis can be rejected, otherwise we fail to reject the null hypothesis.