## Examining Probabilities

Project Part 1: Examining Probabilities

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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.

a) For this part of the assignment, assume that you have distributed a survey containing one 5 point Likert scale question. Likert scale response options are assumed to be equi-distant from each other. Therefore, they can be evaluated at the interval level of measurement. Use this source to identify ONE 5 point Likert scale of response options that you would like to use. List your 5 point scale here

b) Design and write your own question stem to be used with your Likert scale response options listed in #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 Values’ spreadsheet to edit and create your own probability distribution table for your 5 response option values for the random variable question in a) and b) above. Be sure to label the random variable outcomes, in your probability distribution table, using your selected response options. 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) The Excel ‘Generating Values’ spreadsheet, additionally generates 60 random values, based on your probability distribution table created in #1 above. It also creates a frequency distribution table based on these 60 values. Copy, paste, and APA format your completed frequency distribution table here.

3) Generate ONE appropriate chart (your choice) using your frequency distribution table from #2. Copy and paste your chart here. Ensure that it is APA formatted.

4) Write one insightful interpretation, related to your survey question results, (Use APA in-text formatting) of your chart in #3. Use complete sentences.

Binomial Probability Distribution

A binomial distribution has the following function associated with it:

Figure 1

Binomial Distribution Function

You do not have to calculate using this formula. Excel handles this for you. 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.

a) Now 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. Google ‘examples of binomial variables’. Select an example variable. List your variable here, a feasible probability of a success p, and provide the link to the online source you used.

b) With your binomial variable , listed in a) above, list your own 5 questions and response options (what respondents will be asked to select from when answering the question) that fit the binomial criteria here in Table 1.

Table 1

Survey Questions and Response Options

Question Number

Question

Response Options

5) 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

Is there a fixed number of administrations of the survey? If so, how many (write the actual count or n) ?

Are there only 2 possible response choices (Yes or no)?

Is there a single probability of success , that is the same of all questions, that is applied to the likelihood of a favorable response? (Yes or no) If so, what is the value for p?

Will the respondent responses to your questions be independent of each other? How can you ensure this when it is administered?

6) Reference the ‘Generating Survey Data in Excel’ Workbook and the ‘Binomial’ 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 100 randomly selected respondents.

7) Use the =COUNTIF formula in Excel to count the number of 1 and 0 responses for each of the 5 survey questions. Calculate the count and percent of 1 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

Percent of 1 responses

8) How closely related is your expected binomial probability value p and the percentages of 1 responses for each question in your Table 3 above? Explain.

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

10) Google ‘Willie Mays stats’. Find his AB (at bat) and H (hits) numbers for 1968. Assuming that the variable ‘hits at bat’ (where hits is considered a success) follows a binomial distribution, if Willie Mays could of had 1000 ABs in 1968, what would be his predicted number of hits (rounded to the nearest highest whole number) at an alpha value of .05?

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