# Statistics Lab Report 2611 Essay

Published: 2020-02-15 08:12:09
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The purpose of this lab intends to explain the process and impacts of confidence and prediction interval techniques and procedures by learning through online tutorials, examples, and quizzes.

Procedures

This lab was conducted in a controlled, computer environment with access to SAS software and applications. Instructions for the lab were provided in .pdf form and included procedures for accessing private applications in SAS. Additionally, tutorials and quizzes were administered using an applet available at http://www.wpi.edu/Academics/ATC/Collaboratory/LOs/Gagnon/PItutor/index.html and http://www.wpi.edu/Academics/ATC/Collaboratory/LOs/Gagnon/CIpQuiz/index.html.

Prediction Intervals

A tutorial was given to help explain the process and purpose of prediction intervals. Following the tutorial, a quiz was taken. The results from the quiz are shown in Figure 1.

Figure 1: Results from online quiz #1.

The purpose of a prediction interval is to tell you where you can expect the next data point to be. SAS computes the prediction interval using equation 5.11, shown below. Ynew-ÏƒYnew-Ynewtn-1,1+L2,Ynew+Ïƒ(Ynew-Ynew)tn-1,1+L2,

The assumptions of this formula are that the {âˆˆi} are independent N(0,Ïƒ2) random variables. Following the instructions from the lab report, SAS was used to build a data containing the measurements of the speed of light. Parameters for the application are C = 0.90. The results of this application are shown in Figure 2.

Figure 2: Prediction Interval using SAS with application SASDATA.SOL. C = 0.90 The width of the prediction interval is 2.9996 2.9972 = .0024. The width of the confidence interval is 2.9985 2.9983 = .0012. The width of the prediction interval is exactly twice as large (wide) as the confidence interval. If the confidence interval is increased to C = 0.95 (95%), the result is an increase in the prediction interval. This is illustrated in Figure 3.

Figure 3: Prediction Interval using SAS with application SASDATA.SOL. C = 0.95 As shown in Figure 3, the prediction interval is 2.9998 2.997 = .0028. This means that an increase in the level of confidence will result in an increase in the width of the prediction interval. Based on equation 5.11, the center of the prediction interval is the mean = 2.9984. Confidence intervals for a population proportion

A tutorial was given to help explain the process and purpose of confidence intervals. Following the tutorial, a quiz was taken. The results from the quiz are shown in Figure 4.

Figure 4: Results from online quiz #2.
The macro BIEXACT uses in SAS to compute the exact confidence intervals for a population proportion is shown below. If Y > 0, PD = y=Ynn!y!n-y!PDy(1-PD)n-y=1-L2
If Y = 0, PD = 0,
If Y < n, PU = y=0Yn!y!n-y!PUy(1-PU)n-y=1-L2
And if Y = n, PU = 1
Using the BIEXACT macro in SAS, a survey of 23 people was conducted and 7 of them are planning on seeing Transformers 3. The results of using a 95% confidence interval are shown in Figure 5.

Figure 5: Confidence Interval using SAS Software and application macro BIEXACT. Sample size = 23, success number = 7, confidence level = .95. This confidence interval tells you how well you have estimated the mean. In this case, a confidence level of 95% demonstrates that the resulting intervals represent the true population parameters 95% of the time. Using the binomial model, we are assuming that the total number of sample items has approximately a binomial distribution.

Conclusion

This lab helped me learn the basics of confidence and prediction intervals and the procedures involved in calculating those intervals. I was able to learn from online tutorials about how to appropriately calculate a prediction or confidence interval, and reassured my knowledge with a quiz. Additionally, I learned that by increasing the sample size will decrease prediction interval, and that increasing the confidence interval will result in an increase in the prediction interval.

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