# l2 - STAT 350 Fall 2008 1 Give the side-by-side histograms...

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STAT 350 – Fall 2008 Lab #2 – SOLUTION 1. Give the side-by-side histograms for ,25 N x and ,100 N x . 53 52 51 50 49 48 40 30 20 10 0 53 52 51 50 49 48 Normal25 mean Frequency Normal100 mean Histogram of Normal25 mean, Normal100 mean (i) What would you have expected the statistic to be (what value)? I would expect the sample mean to be close to the population mean. The samples came from a Normal( μ = 50, σ = 5) distribution which has mean 50, so I would expect the statistic to be 50. (ii) What is the shape of each distribution? Each distribution is approximately symmetric and bell-shaped (iii) What is the center of each distribution (the mean of the distribution, see Step 8 in the directions)? Answers will vary because the data was simulated independently by each student, but answers should be close to 50. For the data graphed above, the centers were 49.962 and 50.012 respectively. (iv) Does the center appear to be affected by increasing the sample size. If so, how? No – the center was not [significantly] affected by increasing sample size. (v) What is the standard deviation of each distribution (see Step 8 in the directions)? Answers will vary because the data was simulated independently by each student, but answers should be close to 5 n (1 and 0.5). For the data graphed above, the standard deviations were 1.017 and 0.508 respectively. (iv) Does the standard deviation appear to be affected by increasing the sample size. If so, how?

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l2 - STAT 350 Fall 2008 1 Give the side-by-side histograms...

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