Question

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 Ha 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 H, in favor of Ha? 50, what will be our c: (6 pts) Consider different cases where we observe T = 10, T = 90 and T corresponding conclusions given the choice of RR we made in part b?

Answer 1

P a) Let' be the chance of getting head, the null and alternative hypothesis based the question is Ho: P=0.5 NS. Han pao.5 na 100 The region rejection region will help us reject Ho in favour of is 2.T320 the alternative hypothesis in @ is left tail. Ha brause 1 Talo, when T=10 5 falls under the critical region. Henar reject the null hypothesis and conclude that the coin has larger chance getting fails than heads, of 1:2 When Tago and T=50. Both the observed T=90 and T250 do not fall at critical region. Hence, fail to reject the null hypothesis and conclude that the coin does not have larger chance of getting fails than heads.