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Class 5 - c_i_demo

# Class 5 - c_i_demo - Introduction The simulation on the...

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Introduction Page 1 The simulation on the following two pages generates a sample of 9 observations for a variable X that has a standard normal distribution with mean 0 and standard deviation 1. This distribution of X is graphed used in dark blue . The values for the 9 sample observations are indicated by the pink dots at the top. The distribution of the sample mean appears in yellow and is normal with mean 0 and standard deviation 1/3. The location of sample mean (the average of the 9 sample observations) is at the light blue spike . The sample data are used to calculate an 80% confidence interval assuming that the phenomenon standard deviation is unknown. The upper and lower limits are graphed by a green line . A new set of observations is created each time the F9 function key is pushed. Notice that the width of the confidence interval will change because the sample standard deviation varies from sample to sample. Also notice that the 80% confidence interval generally contains 0 which is the phenomenon mean, but not always. If fact with an 80% interval one would expect 0 to be outside the interval 20% of the time. A 95% confidence interval is added on the second sheet and one would expect it to only have 0 outside of the interval 5% of the time. Its limits are graphed with a brown line . A 99% confidence interval is also added on the second sheet and one would expect it to only have 0 outside of the interval 1% of the time. Its limits are graphed with a red line .

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80 % C.I. for mean Page 2 1 2 3 4 5 6 7 8 9 -1.05 -0.66 -0.47 0.04 0.04 0.1 0.86 0.91 1.27 < Ordered Sample Observations 80% Confidence Interval for the Phenomenon Mean Phenomenon Mean = 0 Sample Mean + Table Value * Standard Error Lower Upper 0.12 + 1.4 * 0.78 Limit Limit 0.12 + 0.36 Interval Contains 0 -0.25 0.48 0.04 1.27 0.1 0.86 -1.05 -0.47 -0.66 0.91 0.04 Height on Graph = 1.3 1.4 1.5 Rounded Value = 0.12 -0.25 0.48 X on of X of X-bar Freque Sample e Mean 80% Co 95% Co 99% Confidence Limits -3 0 0 0 0 0 0 0 0 95% 95% 99% 99% -2.99 0 0 0 0 0 0 0 0 Lower Upper Lower Upper -2.98 0 0 0 0 0 0 0 0 Limit Limit Limit Limit -2.97 0 0 0 0 0 0 0 0 -0.48 0.71 -0.75 0.99 -2.96 0 0 0 0 0 0 0 0 -0.48 0.71 -0.75 0.99 -2.95 0.01 0 0 0 0 0 0 0 -2.94 0.01 0 0 0 0 0 0 0 -2.93 0.01 0 0 0 0 0 0 0 -2.92 0.01 0 0 0 0 0 0 0 -2.91 0.01 0 0 0 0 0 0 0 -2.9 0.01 0 0 0 0 0 0 0 -2.89 0.01 0 0 0 0 0 0 0 -2.88 0.01 0 0 0 0 0 0 0 -2.87 0.01 0 0 0 0 0 0 0 -2.86 0.01 0 0 0 0 0 0 0 -2.85 0.01 0 0 0 0 0 0 0 -2.84 0.01 0 0 0 0 0 0 0 -2.83 0.01 0 0 0 0 0 0 0 -2.82 0.01 0 0 0 0 0 0 0 -2.81 0.01 0 0 0 0 0 0 0 -2.8 0.01 0 0 0 0 0 0 0 -2.79 0.01 0 0 0 0 0 0 0 -2.78 0.01 0 0 0 0 0 0 0 -2.77 0.01 0 0 0 0 0 0 0 -2.76 0.01 0 0 0 0 0 0 0 -2.75 0.01 0 0 0 0 0 0 0 -2.74 0.01 0 0 0 0 0 0 0 -2.73 0.01 0 0 0 0 0 0 0 -2.72 0.01 0 0 0 0 0 0 0 -2.71 0.01 0 0 0 0 0 0 0 -2.7 0.01 0 0 0 0 0 0 0 -2.69 0.01 0 0 0 0 0 0 0 -2.68 0.01 0 0 0 0 0 0 0 -2.67 0.01 0 0 0 0 0 0 0 -2.66 0.01 0 0 0 0 0 0 0 -2.65 0.01 0 0 0 0 0 0 0 -2.64 0.01 0 0 0 0 0 0 0 -2.63 0.01 0 0 0 0 0 0 0 -2.62 0.01 0 0 0 0 0 0 0 -2.61 0.01 0 0 0 0 0 0 0 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 Distribution of X Distribution of X- bar Sample Values Sample Mean 80% Confidence Limits 9
80 % C.I. for mean Page 3 -2.6 0.01 0 0 0 0 0 0 0 -2.59 0.01 0 0 0 0 0 0 0 -2.58 0.01 0 0 0 0 0 0 0 -2.57 0.01 0 0 0 0 0 0 0 -2.56 0.02 0 0 0 0 0 0 0 -2.55 0.02 0 0 0 0 0 0 0 -2.54 0.02 0 0 0 0 0 0 0 -2.53 0.02 0 0 0 0 0 0 0 -2.52 0.02 0 0 0 0 0 0 0 -2.51 0.02 0 0 0 0 0 0 0 -2.5 0.02 0 0 0 0 0 0 0 -2.49 0.02 0 0 0 0 0 0 0 -2.48 0.02 0 0 0 0 0 0 0 -2.47 0.02 0 0 0 0 0 0 0 -2.46 0.02 0 0 0 0 0 0 0 -2.45 0.02 0 0 0 0 0 0 0 -2.44 0.02 0 0 0 0 0 0 0 -2.43 0.02 0 0 0 0 0 0 0 -2.42 0.02 0 0 0 0 0 0 0 -2.41 0.02 0 0 0 0 0 0 0 -2.4 0.02 0 0 0 0 0 0 0 -2.39 0.02 0 0 0 0 0 0 0 -2.38 0.02 0 0 0 0 0 0 0 -2.37 0.02 0 0 0 0 0 0 0 -2.36 0.02 0 0 0 0 0 0 0 -2.35 0.03 0 0 0 0 0 0 0 -2.34 0.03 0 0 0 0 0 0 0 -2.33 0.03 0 0 0 0 0 0 0 -2.32 0.03 0 0 0 0 0 0 0 -2.31 0.03 0 0 0 0 0 0 0 -2.3 0.03 0 0 0 0 0 0 0 -2.29 0.03 0 0 0 0 0 0 0 -2.28 0.03 0 0 0 0 0 0 0 -2.27 0.03 0 0 0 0 0 0 0 -2.26 0.03 0 0 0 0 0 0 0 -2.25 0.03 0 0 0 0 0 0 0 -2.24 0.03 0 0 0 0 0 0 0 -2.23 0.03 0 0 0 0 0 0 0 -2.22 0.03 0 0 0 0 0 0 0 -2.21 0.03 0 0 0 0 0 0 0 -2.2 0.04 0 0 0 0 0 0 0 -2.19 0.04 0 0 0 0 0 0 0 -2.18 0.04 0 0 0 0 0 0 0 -2.17 0.04 0 0 0 0 0 0 0 -2.16 0.04 0 0 0 0 0 0 0 -2.15 0.04 0 0 0 0 0 0 0 -2.14 0.04 0 0 0 0 0 0 0 -2.13 0.04 0 0 0 0 0 0 0 -2.12 0.04 0 0 0 0 0 0 0 -2.11 0.04 0 0 0 0 0 0 0 -2.1 0.04 0 0 0 0 0 0 0 -2.09 0.04 0 0 0 0 0 0 0 -2.08 0.05 0 0 0 0 0 0 0

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80 % C.I. for mean Page 4 -2.07 0.05 0 0 0 0 0 0 0 -2.06 0.05 0 0 0 0 0 0 0 -2.05 0.05 0 0 0 0 0 0 0 -2.04 0.05 0 0 0 0 0 0 0 -2.03 0.05 0 0 0 0 0 0 0 -2.02 0.05 0 0 0 0 0 0 0 -2.01 0.05 0 0 0 0 0 0 0 -2 0.05 0 0 0 0 0 0 0 -1.99 0.06 0 0 0 0 0 0 0 -1.98 0.06 0 0 0 0 0 0 0 -1.97 0.06 0 0 0 0 0 0 0 -1.96 0.06 0 0 0 0 0 0 0 -1.95 0.06 0 0 0 0 0 0 0 -1.94 0.06 0 0 0 0 0 0 0 -1.93 0.06 0 0 0 0 0 0 0 -1.92 0.06 0 0 0 0 0 0 0 -1.91 0.06 0 0 0 0 0 0 0 -1.9 0.07 0 0 0 0 0 0 0 -1.89 0.07 0 0 0 0 0 0 0 -1.88 0.07 0 0 0 0 0 0 0 -1.87 0.07 0 0 0 0 0 0 0 -1.86 0.07 0 0 0 0 0 0 0 -1.85 0.07 0 0 0 0 0 0 0 -1.84 0.07 0 0 0 0 0 0 0 -1.83 0.07 0 0 0 0 0 0 0 -1.82 0.08 0 0 0 0 0 0 0 -1.81 0.08 0 0 0 0 0 0 0 -1.8 0.08 0 0 0 0 0 0 0 -1.79 0.08 0 0 0 0 0 0 0 -1.78 0.08 0 0 0 0 0 0 0 -1.77 0.08 0 0 0 0 0 0 0 -1.76 0.08 0 0 0 0 0 0 0 -1.75 0.09 0 0 0 0 0 0 0 -1.74 0.09 0 0 0 0 0 0 0 -1.73 0.09 0 0 0 0 0 0 0 -1.72 0.09 0 0 0 0 0 0 0 -1.71 0.09 0 0 0 0 0 0 0 -1.7 0.09 0 0 0 0 0 0 0 -1.69 0.1 0 0 0 0 0 0 0 -1.68 0.1 0 0 0 0 0 0 0 -1.67 0.1 0 0 0 0 0 0 0 -1.66 0.1 0 0 0 0 0 0 0 -1.65 0.1 0 0 0 0 0 0 0 -1.64 0.1 0 0 0 0 0 0 0 -1.63 0.11 0 0 0 0 0 0 0 -1.62 0.11 0 0 0 0 0 0 0 -1.61 0.11 0 0 0 0 0 0 0 -1.6 0.11 0 0 0 0 0 0 0 -1.59 0.11 0 0 0 0 0 0 0 -1.58 0.11 0 0 0 0 0 0 0 -1.57 0.12 0 0 0 0 0 0 0 -1.56 0.12 0 0 0 0 0 0 0 -1.55 0.12 0 0 0 0 0 0 0
80 % C.I. for mean Page 5 -1.54 0.12 0 0 0 0 0 0 0 -1.53 0.12 0 0 0 0 0 0 0 -1.52 0.13 0 0 0 0 0 0 0 -1.51 0.13 0 0 0 0 0 0 0 -1.5 0.13 0 0 0 0 0 0 0 -1.49 0.13 0 0 0 0 0 0 0 -1.48 0.13 0 0 0 0 0 0 0 -1.47 0.14 0 0 0 0 0 0 0 -1.46 0.14 0 0 0 0 0 0 0 -1.45 0.14 0 0 0 0 0 0 0 -1.44 0.14 0 0 0 0 0 0 0 -1.43 0.14 0 0 0 0 0 0 0 -1.42 0.15 0 0 0 0 0 0 0 -1.41 0.15 0 0 0 0 0 0 0 -1.4 0.15 0 0 0 0 0 0 0 -1.39 0.15 0 0 0 0 0 0 0 -1.38 0.15 0 0 0 0 0 0 0 -1.37 0.16 0 0 0 0 0 0 0 -1.36 0.16 0 0 0 0 0 0 0 -1.35 0.16 0 0 0 0 0 0 0 -1.34 0.16 0 0 0 0 0 0 0 -1.33 0.16 0 0 0 0 0 0 0 -1.32 0.17 0 0 0 0 0 0 0 -1.31 0.17 0 0 0 0 0 0 0 -1.3 0.17 0 0 0 0 0 0 0 -1.29 0.17 0 0 0 0 0 0 0 -1.28 0.18 0 0 0 0 0 0 0 -1.27 0.18 0 0 0 0 0 0 0 -1.26 0.18 0 0 0 0 0 0 0 -1.25 0.18 0 0 0 0 0 0 0 -1.24 0.18 0 0 0 0 0 0 0 -1.23 0.19 0 0 0 0 0 0 0 -1.22 0.19 0 0 0 0 0 0 0 -1.21 0.19 0 0 0 0 0 0 0 -1.2 0.19 0 0 0 0 0 0 0 -1.19 0.2 0 0 0 0 0 0 0 -1.18 0.2 0 0 0 0 0 0 0 -1.17 0.2 0 0 0 0 0 0 0 -1.16 0.2 0 0 0 0 0 0 0 -1.15 0.21 0 0 0 0 0 0 0 -1.14 0.21 0 0 0 0 0 0 0 -1.13 0.21 0 0 0 0 0 0 0 -1.12 0.21 0 0 0 0 0 0 0 -1.11 0.22 0 0 0 0 0 0 0 -1.1 0.22 0.01 0 0 0 0 0 0 -1.09 0.22 0.01 0 0 0 0 0 0 -1.08 0.22 0.01 0 0 0 0 0 0 -1.07 0.23 0.01 0 0 0 0 0 0 -1.06 0.23 0.01 0 0 0 0 0 0 -1.05 0.23 0.01 1 1.3 0 0 0 0 -1.04 0.23 0.01 0 0 0 0 0 0 -1.03 0.23 0.01 0 0 0 0 0 0 -1.02 0.24 0.01 0 0 0 0 0 0

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80 % C.I. for mean Page 6 -1.01 0.24 0.01 0 0 0 0 0 0 -1 0.24 0.01 0 0 0 0 0 0 -0.99 0.24 0.01 0 0 0 0 0 0 -0.98 0.25 0.02 0 0 0 0 0 0 -0.97 0.25 0.02 0 0 0 0 0 0 -0.96 0.25 0.02 0 0 0 0 0 0 -0.95 0.25 0.02 0 0 0 0 0 0 -0.94 0.26 0.02 0 0 0 0 0 0 -0.93 0.26 0.02 0 0 0 0 0 0 -0.92 0.26 0.03 0 0 0 0 0 0 -0.91 0.26 0.03 0 0 0 0 0 0 -0.9 0.27 0.03 0 0 0 0 0 0 -0.89 0.27 0.03 0 0 0 0 0 0 -0.88 0.27 0.04 0 0 0 0 0 0 -0.87 0.27 0.04 0 0 0 0 0 0 -0.86 0.28 0.04 0 0 0 0 0 0 -0.85 0.28
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Class 5 - c_i_demo - Introduction The simulation on the...

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