Problem 5. (10 pts: 4,3,3) Data is drawn from a binomial(5, 0) distribution, where 0 is unknown. Here is the table of probabilities p(x | 0) for 3 values of 0: 0 1 2 0 = 0.5 0.031 0.156 0.313 0.313 0.156 0.031 0 = 0.6 0.010 0.077 0.230 0.346 0.259 0.078 0 = 0.8 0.000 0.006 0.051 0.205 0.410 0.328 You want to run a significance test on the value of 6. You have the following: Null hypothesis: 0 = 0.5. Alternate hypotheses: 0 > 0.5. Significance level: o = .1. (a) Find the rejection region. (b) Compute the power of the test for each of the two hypotheses d = 0.6 and 0 = 0.8. (c) Suppose you run an experiment and the data gives r = 4. Compute the p-value of this data.Problem 6. (15 pts: 5,5,5) You have data drawn from a normal distribution with a known variance of 16. You set up the following NHST: . Ho: data follows a N(2, 4?) . HA: data follows a N(u, 43) where / / 2. . Test statistic: standardized sample mean z. . Significance level set to o = .05. You then collected n = 16 data points with sample mean 1.5. (a) Find the rejection region. Draw a graph indicating the null distribution and the rejection region. (b) Find the z-value and add it to your picture in part (a). (c) Find the p-value for this data and decide whether or not to reject Ho in favor of HA-Problem 7. (15 pts) Someone claims to have found a long lost work by Jane Austen. She asks you to decide whether or not the book was actually written by Austen. You buy a copy of Sense and Sensibility and count the frequencies of certain common words on some randomly selected pages. You do the same thing for the 'long lost work'. You get the following table of counts. Word an this that Sense and Sensibility 150 30 30 90 Long lost work 90 20 10 80 Using this data, set up and evaluate a significance test of the claim that the long lost book is by Jane Austen. Use a significance level of 0.1