2. Let X1, ..., Xn be independent and identically distributed continuous random vari- ables whose underlying distributio

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2 Let X1 Xn Be Independent And Identically Distributed Continuous Random Vari Ables Whose Underlying Distributio 1 (203.58 KiB) Viewed 13 times

These are the results of the dataset.
2. Let X1, ..., Xn be independent and identically distributed continuous random vari- ables whose underlying distribution has a unique median m, i.e. there exists a unique number m such that 1 P(X; < m) = P(X; > m) 2 Consider the testing problem Ho: m = mo H:m> mo, for a fixed given number mo. The test statistic T is the number of observations greater than mo: T = #{1 < i < n | X, > mọ}. a. [2] What is the distribution of T under the null hypothesis? To judge the level of a homework assignment, a group of 13 randomly chosen students was asked to make the assignment beforehand. The results can be found in the file “PTS2_assignment6_dataset.csv" on Canvas. Suppose their results are the sample realization of the sample X1, ..., X, discussed at the beginning of this exercise. b. [4] Test Ho: m = 6 against Hų: m > 6 at significance level a = 0.05. N.B. Strictly speaking, the normal approximation is allowed to be used in this exercise. However, because of the small sample size the approximation may not be very good. Therefore, please use an exact calculation. Hint: To find the p-value you can either use the distribution tables in the back of the reader or the cumulative distribution functions in R (like qnorm, qt, qbinom, etc).