seminar q 1 - . Question 1. a. Generate a random variable with 1000 observations using the normal distribution, X~N(50,100) in R. b. Display the distribution of the RV in a histogram. c. What is the mean and standard deviation? d. Presume that what you generated in a. and b. is a population distribution. Now take 10.000 samples with 100 observations in R. e. What would you expect the distribution of the resulting 10,000 sample means to look like? f. Draw a histogram of the sampling distribution and check whether your conjecture is correct. g. What is the mean of that distribution and what is the standard error? h. Which statistical concept have you just demonstrated through this simulation? Question 2. Do the same steps a-g as in question 1 but now generate a random variable with n=1000 using the Poisson distribution with =1 (hint: R calls this parameter lambda) What distribution does the sampling distribution approximate?

seminar q 2- Do the same steps a-g as in question 1 but now generate a random variable with n=1000 using the Poisson distribution with =1 (hint: R calls this parameter lambda) What distribution does the sampling distribution approximate?

} C. a. Test the hypothesis from seminar question 1 again using R b. Now create a RV x from a sample with n=1000, drawn from a population with mean 530 and standard deviation 90, and adapt the function to test the hypothesis that the population mean is 525. What do you decide? Now create a new RV y with n=35, drawn from a population with mean 530 and standard deviation 90. Test the hypothesis that the population mean is 525 again. d. Create a function that performs one-sided hypothesis tests of means (again, by varying the function defined at the beginning) e. Draw a sample of n=64 from a population with mean 25000 and standard deviation 750. Test the one-sided hypothesis in seminar question 2 again. What do you decide? Is this the correct decision or are you making an error? If yes, which type of error