Applied Learning Research Project

Project Part 1: Examining Probabilities

Directions: Respond to the prompts below. Follow the ‘Do Not’ and ‘Do’ instructions.

DO NOT : · Upload your Excel workbook to Moodle · Copy and paste your dataset into this document · Upload your work as a Word document in Moodle

DO · Paste or type your responses directly into this document · Save your completed work as a PDF file · Upload your only your PDF file to Moodle

A random variable is a variable whose value is determined by the outcomes of a probability experiment. For every random variable, a probability distribution can be defined. A probability distribution represents the probability of occurrence for each value of the random variable. Associated with a probability distribution, is a function that can be used to calculate the probability values. The sum of all the probabilities, for all possible values of a single random variable, should sum to 1.

Probability Distribution

1) Reference the ‘Generating Survey Data in Excel’ Excel workbook resource associated with this assignment. Examine the ‘Generating Values’ spreadsheet. Feel free to edit/update this spreadsheet while addressing the requirements for this prompt.

Use what you learned from the ‘Generating Survey Data in Excel’ spreadsheet to edit and create your own probability distribution table where there are 6 outcome values for the random variable. Feel free to label the random variable outcomes whatever you choose. Feel free to assign the probability distribution probability values, associated with the random variable outcome labels, appropriately in a manner that you choose. Copy, paste, and APA format your completed probability distribution table here.

2) In Excel and using the process outlined on the ‘Generating Values’ spreadsheet, generate 60 random values, based on your probability distribution table created in #1 above. To do this, you will likely need to update the Excel formula in that begins in cell F4. The formula is presented below

=INDEX(A$7:A$11,COUNTIF(C$7:C$11,"<="&RAND())+1)

Update ‘A$7:A$11’ to ensure it captures all of your random variable outcomes

Update ‘C$7:C$11’ to ensure it captures all of your cumulative probability values

Once you update the formula, use the Fill Handle to drag the formula to generate the 60 random values that you need.

3) Then create a frequency distribution table based on these 60 values. Use the format in the ‘Generating Values’ spreadsheet. You may need to edit the Excel formula beginning in cell J8. That formula is presented below:

=COUNTIF(F$7:F$24,I8)

Update ‘F$7:F$24’ to ensure it captures all of your 60 values

Use the Fill Handle to copy your updated formula across all rows of the frequency variable column

4) Copy, paste, and APA format your completed frequency distribution table here.

5) Generate ONE appropriate chart (your choice) using your frequency distribution table. Copy and paste your chart here. Ensure that it is APA formatted.

Binomial Probability Distribution

A binomial distribution has the following function associated with it:

Figure 1

Binomial Distribution Function

The mathematics underlying this function are built into Excel. However to ensure that the results Excel generates are reliable, you must first check to ensure that your probability experiment satisfies the Binomial Probability usage criteria.

6) You are being asked to design a small survey (questionnaire ) of questions for your business purpose of choice. However, you must generate a survey of 5 questions where the probability of the occurrence of the response options can be calculated using the binomial probability formula. List your 5 questions and response options (what respondents will be asked to select from when answering the question) , that fit this criteria, here in Table 1.

Table 1

Survey Questions and Response Options

Question Number	Question	Response Options

7) Explain, using complete sentences, how it is that the binomial probability formula usage criteria will be met , in your proposed survey administration and design, when calculating the probability of responses to your 5 survey items. Type your explanations below in Table 2.

Table 2

Explanations in Support off Binomial Probability Usage Criteria

Binomial Probability Usage Criteria	Explain
Will there be a fixed number of administrations of the survey? If so, how many?
Are there only 2 possible response choices?
Is there a single probability of success , that is the same of all questions, that is applied to the likelihood of a favorable response? If so, what is it?
Will the respondent responses be independent of each other? How will you ensure this?

8) Reference the ‘Generating Survey Data in Excel’ spreadsheet resource associated with this assignment. Use the Data Analysis Toolpak to generate the numerical values associated with the binomial probability related response options to your 5 survey questions. Assume that you will administer the survey to 50 randomly selected respondents.

9) Use the =COUNTIF formula in Excel to count the number of 1 and 0 responses for each of the 5 survey questions. Calculate the percent of 1 and 0 responses for each of the 5 survey questions. Type your results into Table 3 below.

Table 3

Frequency and Percent of 1 and 0 Responses to Survey Questions

	Question1	Question2		Question3	Question4	Question5
Total Number of 1 responses
Total Number of 0 responses
Percent of 1 responses
Percent of 0 responses

10) Is there any relationship between the binomial probability of a 1 response and the percentages of 1 responses in your table above? Explain.

11) In Excel, generate a bar chart for the percent of 1 and 0 responses for your 5 survey items. Correct APA formatting is expected. Copy and paste your chart here.