Question

PROBLEM SET 2 (Due date: after the class on June 11) 1. Suppose that the mean price per liter of regular gas(oline) sold in Korea is 1,200 Won Now assume the population mean price per liter is 1, 200, and the population standard deviation is o = 400. Suppose that a random sample of 500 gas stations will be selected, and a sample mean price per liter will be computed for data collected from the 500 gas stations. (a) Show the sampling distribution of the sample mean X where X is the sample mean price per liter for the 500 gas stations (b) What is the probability that the simple random sample will provide a sample mean within 20 won, of the population mean (±20)? (c) What is the probability that the simple random sample will provide a sample mean within 10 won, of the population mean (10)? (d) Suppose you can get a chance to select a random sample of 1,000 gas stations, and then denote the sample mean based on the 1,000 gas station as X1000, and the sample mean based on the 500 gas station as X 500- Are they both unbiased estimators? (e) Calculate the variance of X1000- (f) Can you conclude that being able to collect more gas stations' data will provide more accurate information? Why or why not? 2. A record store owner knows that 25% of customers entering her store make a purchase. Consider a random sample consisting of 100 customers who entered the store. (a) What is the mean and variance of the sample proportion of customers making purchase? (b) What is the probability that the sample proportion is less than 0.20? (e) She caleulated the probability that the sample proportion is lower than tion a, and the probability turned out 0.05. Then what is this number a? propor- 3. It is found that the starting salaries of the graduates from KU follow normal distribution with mean 25 (million won) and standard deviation 4 (million won). For those who have started the job this year, a random sample of 16 is selected. (a) What is the probability that the sample mean of the 16 samples is more than 30 (million won)? (b) The probability is 0.1 that the sample mean is less than how much won? (e) What is the probability that the sample variance is more than twice the population variance? (d) The probability is 0.05 that the sampel standard deviationj exceeds what number? 3 다음으로 열기 인쇄

Answer 1

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