(a) Suppose x = (x_1, x_2, ..., x_n) is a random sample from a distribution havi

Question

(a) Suppose x = (x_1, x_2, ..., x_n) is a random sample from a distribution having median theta. Recall that sample median is used as a point estimate of the population median. Describe how would you obtain a 95% percentile bootstrap confidence interval for based on 1000 bootstrap samples. (b) Suppose x = (x_1, x_2, ..., x_n) and y = (y_1, y_2, ..., y_n) are observed samples from N(mu_1, sigma^2) and N(mu_2, sigma^2). Describe how to obtain the bootstrap p-value for testing H_0: mu = mu_2 versus H_1:mu_1 > mu_2 based on 1000 bootstrap samples.

Explanation / Answer

Step 1: Generate the samples sizes n1 and n2 from the sample x and y respectively with replication.

Step 2: Compare the mean of the Step 1.

Step 3 : Estimate the p-value from Step 2.

Step 4. Replicate Steps 1 to 3 1000 times.

Step 5. Find the mean p-value from 1000 replicate p-values. This p-value is your required p-value.

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