Question

Q2 (15) 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:(4 pts) Let p be the chance of getting heads, write down the alternative hypothesis H, and the null hypothesis Ho in terms of p. b: (5 pts) 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 Ho in favor of H,? c: (6 pts) 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?

Answer 1

a: Let p be the chances of getting heads and q be the chances of getting tails. The hypotheses are, H. pa H:p<9 b: Let I be the number of heads as the test-statistic. The null hypotheses are always rejected, when the value of test-statistic is greater than the critical value. So, T 280 rejection region will help to reject H, in favor of H,

c: when T =10, the null hypothesis is not rejected. When T = 90, the null hypothesis is rejected in favor of alternative hypothesis. When T = 50, the null hypothesis is not rejected in favor of alternative hypothesis.