ST3003: Normal Distribution
Overview
For this Performance Task, you will compute confidence intervals and hypothesis tests for normal distributions.
Professional Skills: Written Communication, Interpreting Data & Quantitative Fluency and Technology are assessed in this Competency.
Your response to this Assessment should:
- Reflect the criteria provided in the Rubric.
- Adhere to the required assignment length.
This Assessment requires submission of one file, a completed report including all computations, graphs, and explanations. Save your files as follows:
- Save the report as ST3003_firstinitial_lastname (for example, ST3003_J_Smith).
You may submit a draft of your assignment to the Turnitin Draft Check area to check for authenticity. When you are ready to upload your completed Assessment, use the Assessment tab on the top navigation menu.
Instructions
Before submitting your Assessment, carefully review the rubric. This is the same rubric the assessor will use to evaluate your submission and it provides detailed criteria describing how to achieve or master the Competency. Many students find that understanding the requirements of the Assessment and the rubric criteria help them direct their focus and use their time most productively.
Open the Body Data file under “Elementary Statistics, 13th edition” in Statdisk. This file contains information on the measurements of a sample of 300 individuals. The population mean systolic blood pressure is 124.7 with a variance of 211.10. The population standard deviation is said to be roughly 14.5. For this exercise, refer to pages 7, 11, and 12 of the Statdisk User Manual document. Be sure to enter the population standard deviation in the appropriate box.
- Given that the systolic blood pressure is normally distributed, calculate the descriptive statistics for this column of data and paste it here. Your calculations should include:
- Mean
- Median
- Mode
- Variance
- Standard Deviation
- Range
- Calculate a 90%, 95%, and 99% confidence interval and paste your results here. As the level of confidence increases, what happens to the width of the confidence interval? Does it increase or decrease? Explain why this would happen.
- Since the confidence interval relates to our willingness to calculate a confidence interval that does not include the population mean, what does this tell us about the width of the interval? Give an example of where you might use a 99% confidence interval and another where a 90% interval would be appropriate.
- Based on the data in the “Measurement Data” file, you think that the mean systolic blood pressure is less than the national average of 124.7. Perform a hypothesis test at the 0.05 level of significance to verify this. Use the four-step process outlined in the file “Hypothesis Test for a Population Mean” in the classroom.