Sta2023 application 2: sample data and inferential statistics

Part 1: Written Introduction

Write an introduction to this application. Discuss how sample data values can be used to

estimate population values. Refer to the textbook or class notes to describe the basic

components of the application and the statistical concepts that are applied. The introduction

should be at least 50 words and be written with proper grammar and spelling.

Part 2: Collect and Organize Random Data Values and their Summary Statistics

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 (or

.pdf) document.

1. All relevant information is posted in the course website (Falcon Online). Your instructor will

assign a data set to you in order to complete this application.

For the purpose of this application, treat the data set as if it represented the given random

variable and was a valid random sample gathered by a researcher from a normally distributed

population. The sample data was actually found with an online Gaussian random number

generator that creates randomly distributed data values. The random number generator

simulates the results of a researcher finding those values through observation or

experimentation.

2. Use technology (Excel, graphing calculator, etc.) to sort the 25 sample data values from low

to high. Use Excel or similar software to put the data into a table with 5 columns and 5 rows.

Label this “Table 1: Sorted Set of Sample Data.”

3. Use technology to find the mean, median, standard deviation, and variance of the sample

data organized in Table 1 (from step 2 above). Put these values, plus the range 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 median and range do not generally have symbols so the terms “Median” and

“Range” can be used in the left column. The statistics should be rounded properly (one more

decimal place than the data). Label this “Table 2: Important Statistics.”

STA2023 Application 2 (2016-17) 2

3. Use the sample mean and standard deviation to find the minimum and maximum usual

values. Put these values in a table with the proper symbol(s) in the left column and the values

in the right column. Label this “Table 3: Minimum and Maximum Usual Values.”

4. Choose a confidence level similar to one found in the homework (such as 90%, 95% or 99%;

do not use the confidence level from the posted example). 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 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 1.”

5. Choose another confidence level similar to one found in the homework (do not use the

confidence level from the posted example). 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 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 5: Confidence Interval 2.”

Part 3: Summary

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. Write about the concepts in the application rather than the steps followed.

Discuss the data values, their distribution, and whether there are any unusual values.

Discuss why the t-distribution is used and how the requirements for creating a

confidence interval are met, including comments on sample size.

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.

Compare the 2 different confidence intervals, noting the differences in the critical values

and errors.

Does either one or both of the confidence intervals contain the mean that was used by

the random number generator to create the sample data set?