Application: Inferential Statistics

The completed application should be submitted as a single document

Purpose: The purpose of this assignment is to collect and organize a random sample of data values and then create two different confidence interval estimates of the population mean. The information will then be analyzed in a written summary.

Part 1: Generate and Organize a Set of Random Data Values

Methods: Use Excel (or similar software) to create the tables. Then copy the items and paste them into a Word document. The tables should be formatted vertically, have borders, and be given the labels and titles stated in the assignment. The proper symbols should be used. Do not submit this assignment as an Excel file. The completed assignment should be a Word document.

If you have completed Application successfully, you can use the data and statistics from that application to complete steps 1 and 2 below. Otherwise start with step 1.

The sample data will be found by using an online random number generator. Use the link below or any other random generator of your choice.

Set the random number generator to find numbers between 1 and 75. Repeat the simulation 40 times, recording the number for each repetition. Use technology (Excel, graphing calculator, etc.) to sort the data from low to high. Use Excel or similar software to put the data into a table with 4 columns and 10 rows. Label this "Table 1: Sorted Set of Random Data."

Use technology to find the mean and standard deviation. Put the mean, standard deviation, and sample size into a table with the proper symbol in the left column and the value of the statistic in the right column. The statistics should be rounded properly. Label this "Table 2: Important Statistics."

Choose a confidence level similar to one found in the homework (such as 90%, 95% or 99%). Based on the confidence level, find the critical value and calculate the margin of error. In a table, state the first confidence level, the point estimate, the critical value, margin of error, and confidence interval. Put the proper symbols or term in the left column and the value of the statistic or properly formatted confidence interval in the right column. The statistics and confidence interval should be rounded properly. Label this "Table 3: Confidence Interval 1."

Choose another confidence level similar to one found in the homework. Based on the second confidence level, find the critical value and calculate the margin of error. In a table, state the second confidence level, the point estimate, the critical value, margin of error, and confidence interval. Put the proper symbols or term in the left column and the value of the statistic or properly formatted confidence interval in the right column. The statistics and confidence interval should be rounded properly. Label this "Table 4: Confidence Interval 2."

Part 2: Written Introduction and Summary

Write an introduction to this application. Discuss how the data values were found and why they are random. Describe the basic components of the application and the statistical concepts that will be applied. The introduction should be at least 50 words and be written with proper grammar and spelling.

Write a summary of the application, considering the following topics. The summary should be at least 150 words and be written with proper grammar and spelling. Refer to the tables (by label and number) throughout the summary. Use the proper statistical terms and symbols in the summary.

Discuss the point estimate and how it is determined.
Discuss the relationship between the confidence level and the critical value.
Discuss the error and how the confidence interval is created. Do not describe the arithmetic steps.
Interpret each confidence interval using the concepts presented in the textbook.
Compare the 2 different confidence intervals, noting the differences in the critical values and errors.

The population for the data in this assignment is the numbers from 1 to 75. The population mean is µ=38 and the population standard deviation is 21.6. (How is this determined?) Compare the sample mean and standard deviation to those of the population. Does either one or both of the confidence intervals contain the population mean?