Then select the appropriate variable to graph and click "OK". In Minitab Express, you make the normal probability plot by going to Graphs -> Probability Plot, then selecting "Simple" under "Single Y Variable". The curvature in the normal probability plot will likely be rather apparent, perhaps easier to see than the skewness in the histogram. Then plot a histogram (you should see a little skewness) and a normal probability plot. Finally, to see how things look when the data are closer to normal but not quite normal, simulate 500 values from the chi-square distribution (don't worry that you don't know yet what this is) by going to Calc -> Random Data -> Chi-Square. Try the same think for a uniform distribution, from which you can simulate using Calc -> Random Data -> Uniform. This time the histogram should not look bell-shaped, and the normal probability plot should not look straight. Again make a histogram and a normal probability plot. Next try simulating 100 values from the exponential distribution by going Calc -> Random Data -> Exponential. The y-coordinate is the percentile (which will be, say, 30 if 30 percent of the 100 numbers are below the number in question), but plotted on a scale so that the graph should look like a straight line if the data come from a normal distribution. The x-coordinate of the point is the value itself. There will be a point on the graph for each of the 100 simulated values. Go to Graph -> Probability Plot, then click "OK" and select the appropriate variable to graph. To get a normal curve superimposed on the histogram, click inside the histogram, then click the plus sign to the right of the histogram and check the box for "Distribution Fit". Enter 100 for the number of rows in each column, and leave the distribution as "Normal", then click "OK". In Minitab Express, you get this sample by going to Data -> Generate Random Data. If you wish, you can get a normal curve superimposed on your histogram by drawing a histogram "With Fit" rather than a "Simple" histogram. Make a histogram, and you should see approximately a bell-shaped curve, although it will not be perfectly bell-shaped because it is a relatively small sample. Generate 100 rows of data and store the results in, say, C1. ![]() To see how they work, first take a sample of size 100 from a normal distribution by going to Calc -> Random Data -> Normal. Normal probability plots are useful for determining whether a distribution is approximately normal. You will not look at data until a bit later on. You should also gain experience in this lab in understanding when you should expect distributions to be normal.īegin this lab by opening up a blank Minitab worksheet. You will observe the Central Limit Theorem both by simulating random variables and by taking a sample from a real population. , X n are independent and identically distributed (i.i.d.) random variables with expected value μ and standard deviation σ, then the distribution of the mean of these random variables has approximately a normal distribution, with mean μand standard deviation σ/√ n. The Central Limit Theorem states that if n is large and X 1, X 2. Math 11, Lab 6 Lab 6: Sampling distributions and the Central Limit TheoremIn this lab, you will explore the Central Limit Theorem, a result in probability theory that is that basis for most of the statistical inference techniques that we will study.
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