Question

it is common knowledge that a fair coin lands heads up 50% of the time and tails up 50% of the time. for fair coins, a probability of 0 is assigned to the coin landing on its edge. but what if several coins were glued together? a teacher claims that if 10 pennies were glued together and flipped many times, the penny stack would land on heads 25% of the time, tails 25% of the time, and on its edge 50% of the time. to investigate this claim, a student glues 10 pennies together and flips the stack 200 times. the student would like to know if there is convincing evidence that the distribution differs from what the teacher claimed. what are the appropriate hypotheses?
○ ( h_0 ): the distribution of flips is 25% heads, 25% tails, and 50% edge.
( h_a ): the distribution of flips is not 25% heads, 25% tails, and 50% edge.
○ ( h_0 ): the distribution of flips is not 25% heads, 25% tails, and 50% edge.
( h_a ): the distribution of flips is not 25% heads, 25% tails, and 50% edge.
○ ( h_0 ): the distribution of flips is 25% heads, 25% tails, and 50% edge.
( h_a ): the penny stack will not land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.
○ ( h_0 ): the penny stack will not land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.
( h_a ): the penny stack will land on heads 50 times, tails 50 times, and on its edge 100 times when flipped 200 times.

Explanation:

In hypothesis testing for goodness - of - fit (a type of statistical test in the subfield of Statistics), the null hypothesis \(H_0\) represents the claimed distribution. Here, the teacher's claim is that the distribution is 25% heads, 25% tails, and 50% edge. The alternative hypothesis \(H_a\) is the opposite of the null hypothesis, which is that the distribution is not as claimed.

Answer:

\(H_0\): The distribution of flips is 25% heads, 25% tails, and 50% edge. \(H_a\): The distribution of flips is not 25% heads, 25% tails, and 50% edge. (First option)