Suppose we suspect a coin is not fair — we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question. a: Let p be the chance of getting heads, write down the alternative hypothesis Ha and the null hypothesis H0 in terms of p. b: In order to investigate this question, we flip the coin 100 times and record the observation. Suppose we use T = the number of heads as our test statistic, consider two potential rejection regions, 1. T ≥ 80 2. T ≤ 20 Which rejection region will help us reject H0 in favor of Ha? c: Consider different cases where we observe T = 10, T = 90 and T = 50, what will be our corresponding conclusions given the choice of RR we made in part b?
Suppose we suspect a coin is not fair — we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question.
a: Let p be the chance of getting heads, write down the alternative hypothesis Ha and the null hypothesis H0 in terms of p.
b: In order to investigate this question, we flip the coin 100 times and record the observation. Suppose we use T = the number of heads as our test statistic, consider two potential rejection regions, 1. T ≥ 80 2. T ≤ 20 Which rejection region will help us reject H0 in favor of Ha?
c: Consider different cases where we observe T = 10, T = 90 and T = 50, what will be our corresponding conclusions given the choice of RR we made in part b?
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