# Probability & Statistics Background:

Probability: Your good friend owns two small kiosk stores at Newport Mall where she sells a variety of novelty items

—sunglasses, phone cases, jewelry, etc. She has been keeping track of each transaction and sometimes asks

customers to complete a satisfaction survey. She knows that the information she collects might be useful, but

isn’t sure what to do with it or how it might be helpful. When she heard that you are taking an introduction to

statistics course, she asked you how she might make sense of her sales numbers and use them to plan for the

future. She has a specific question for you as well: Statistically speaking, is one kiosk generally doing better

than the other? That is, is there a difference in sales and customer satisfaction between each of her two kiosks?

Because you are such a good friend, you agree to help her. She shows your her books (full of thousands

of transactions and customer surveys) and you take a sample of the following variables: Transactions on a

typical day (measured in dollars) and customer satisfaction rates (where 1 represents “extremely dissatisfied”

and 5 represents “extremely satisfied”). You also are able to determine which kiosks these measurements come

from (either kiosk 1 or kiosk 2). (This data can be found on the course Blackboard website in the assignment

folder “Final Project.” The file name is 106_Final Project Data. You can open it in MS Excel or in SPSS–

whichever you feel comfortable working with).

Your goal for this project is to present your friend with a report that will be useful to her. The report

should cover the following three aspects: 1) Context for the analysis (i.e. sampling procedures, kinds of

variables and levels of measurement), 2) Descriptive statistics (proportion of measurements coming from each

kiosk, measures of central tendency and dispersion, histogram, assessment of normality, etc.) and 3) Probability

estimates for sales given the distribution of transactions. Within each section, be sure to fully respond to each

question prompt.

Academic Help

Your final project should be typed and handed in during the course final exam period. It should be

written in narrative (paragraph) form, have graphs clearly displayed and labeled, and should not contain any

bullet points or incomplete sentences. You should take the tine to find and use the correct statistical symbols

in your word processing program—they exist. Note: You will have to use a statistical software package such

as MS Excel or SPSS to complete parts 1 and 2. Part 3 can only be accomplished by working the problem by

hand. You must attach your handwritten calculations as an appendix to your final report—you will not

receive credit for part 3 unless you do this. Your final project should look professional and as if you were

preparing it for a business client.

## Probability & Statistics

Part I: Context for the analysis

Be sure to address each of the following questions/bullet points:

• Describe the variables involved in the analysis. What kind of variables are they and at what level are

they measured?

• Your friend believes there might be a difference in sales and customer satisfaction between the two

kiosks she owns. Re-state this sentence as a relationship between two variables: Which is the dependent

and which is the independent variable?

• The data in the file represents the sample of sales transactions and customer surveys that you took from

your friend’s records. How did you collect your sample? Describe what sampling method you chose and

how you sampled from your friend’s records. (This is of course hypothetical—you must imagine that

you took the sample yourself). Feel free to use any sampling method covered in class except for a

convenience sample.)

Part II: Descriptive Statistics

Be sure to address each of the following questions/bullet points:

• Give your friend an overview of her total sales numbers and customer satisfaction rates using descriptive

statistics. Then, break each down by kiosk. You may find that a table or a bar chart is useful here.

• Assess each continuous variable for normality. Be sure to include a histogram and outline the procedures

you used to make a determination about the distribution for each continuous variable.

Part III: Probability Estimates

Be sure to address each of the following questions/bullet points. Keep in mind that given the distributions of

total sales and of customer satisfaction, it may not be possible to answer all of your friend’s questions. In fact, at

least one of the questions below cannot be answered, and you must explain why (Hint: Keep in mind the

difference between the distribution of a variable and it’s sampling distribution):

Estimate the probability that on a given day any one customer will spend between 20 and 25 dollars at either of

the kiosks. Then, estimate the probability that on a given day one customer will spend between 15 and 20

dollars at either kiosk 1 or kiosk 2. If it is not possible to do this, explain to your friend why.

Estimate the probability that on a given day any one customer would say that they are “Satisfied” or “Extremely

Satisfied” with their experience at either one of the kiosks. Then, estimate the probability that on a given day

any one customer would say that they are “Satisfied” or “Extremely Satisfied” with their experience at kiosk 1

or kiosk 2. If it is not possible to do this, explain to your friend why.

Your friend wants to decrease the amount of transactions that are under 20 dollars by up-selling those customers

on small items. She also wants to decrease negative ratings by customers. To that end, she wants to know

approximately what percentage of these transactions that her sales person needs to target for up-selling, and

what percentage of these transactions her sales person needs to make sure that customers have an excellent

experience during.

Consider a sample of 32 customers out of your sample of 271. For every 32 random customers who visit either

kiosk 1 or kiosk 2, approximately how many of those need to be target for an up-sale? (In other words, what is

the probability of any sample of any set of 32 customers spending an average of 20 dollars or below for either

kiosk?)

Approximately how many out of a sample of 32 random customers need to be targeted for a great customer

experience at kiosk 1 and kiosk 2 (meaning that they would report being “Extremely satisfied”)? In other words,

what is the probability that a sample of any 32 random customers at either kiosk 1 or 2 will report being less

than “Extremely satisfied?” If it is not possible to do this, explain to your friend why.

Part IV: Conclusion

Based on your analysis, what recommendations do you have for your friend? Does it appear that one kiosk is

doing better than another in terms of sales and customer satisfaction? (Hint: Consider and compare the

probabilities that you just calculated.) What conclusions can you make based on your subjective judgment and

what conclusions can you make that are backed by your statistical analysis?

#### Probability and Statistics

Customer Satisfaction | Total Sales | Sales at kiosk 1 | Sales at kiosk 2 | Satisfaction at kiosk 1 | Satisfaction at kiosk 2 | ||

5 | 11 | 19 | 11 | 5 | 5 | ||

5 | 19 | 22 | 18 | 2 | 3 | ||

3 | 18 | 26 | 10 | 4 | 5 | ||

5 | 10 | 24 | 21 | 5 | 2 | ||

2 | 22 | 17 | 12 | 4 | 4 | ||

4 | 26 | 23 | 10 | 5 | 5 | ||

5 | 24 | 21 | 21 | 5 | 1 | ||

4 | 17 | 15 | 23 | 1 | 5 | ||

2 | 21 | 14 | 18 | 1 | 5 | ||

4 | 12 | 15 | 19 | 1 | 5 | ||

5 | 23 | 25 | 15 | 1 | 5 | ||

5 | 21 | 21 | 25 | 5 | 1.5 | ||

5 | 10 | 20 | 20 | 1 | 1 | ||

1 | 15 | 25 | 14 | 1 | 1 | ||

1 | 14 | 26 | 21 | 2 | 1.5 | ||

1 | 15 | 18 | 20 | 1 | 1 | ||

1 | 25 | 19 | 14 | 1 | 1 | ||

1 | 21 | 26 | 10 | 5 | 1 | ||

5 | 21 | 25 | 22 | 5 | 2.5 | ||

5 | 23 | 23 | 10 | 1 | 3 | ||

5 | 18 | 27 | 20 | 2.5 | 1 | ||

5 | 19 | 21 | 22 | 1 | 1 | ||

5 | 15 | 22 | 16 | 1.5 | 1.5 | ||

1.5 | 25 | 22 | 19 | 3 | 5 | ||

1 | 20 | 25 | 17 | 2.5 | 5 | ||

1 | 20 | 15 | 20 | 5 | 4 | ||

1 | 14 | 27 | 23 | 1 | 1.5 | ||

1 | 25 | 18 | 19 | 1.5 | 5 | ||

1.5 | 21 | 26 | 11 | 3.5 | 1 | ||

2 | 26 | 24 | 22 | 4 | 1 | ||

1 | 18 | 23 | 19 | 5 | 4 | ||

1 | 20 | 19 | 22 | 4 | 2 | ||

1 | 14 | 26 | 20 | 5 | 1 | ||

1 | 10 | 27 | 27 | 3.5 | 3.5 | ||

1 | 19 | 26 | 16 | 1 | 1 | ||

2.5 | 22 | 21 | 26 | 1.5 | 4.5 | ||

5 | 26 | 20 | 13 | 1.5 | 1 | ||

5 | 25 | 16 | 14 | 3.5 | 1 | ||

3 | 10 | 22 | 11 | 4.5 | 2 | ||

1 | 23 | 24 | 23 | 3 | 1.5 | ||

1 | 20 | 26 | 24 | 4 | 1.5 | ||

2.5 | 27 | 24 | 22 | 5 | 2.5 | ||

1 | 21 | 13 | 25 | 1 | 4 | ||

1 | 22 | 25 | 21 | 2 | 4.5 | ||

1.5 | 22 | 26 | 28 | 3.5 | 4 | ||

3 | 22 | 26 | 8 | 5 | 4.5 | ||

2.5 | 25 | 21 | 12 | 4 | 5 | ||

5 | 15 | 24 | 23 | 2.5 | 2.5 | ||

1.5 | 16 | 10 | 23 | 5 | 3 | ||

1 | 27 | 10 | 21 | 1 | 3 | ||

5 | 19 | 19 | 22 | 1 | 4 | ||

1.5 | 18 | 25 | 18 | 3.5 | 4.5 | ||

3.5 | 26 | 9 | 21 | 5 | 4 | ||

4 | 24 | 24 | 23 | 5 | 3.5 | ||

5 | 17 | 25 | 12 | 5 | 4 | ||

5 | 23 | 21 | 17 | 4.5 | 4 | ||

4 | 20 | 24 | 21 | 2 | 5 | ||

1.5 | 23 | 20 | 13 | 4.5 | 3 | ||

5 | 19 | 21 | 20 | 4 | 5 | ||

4 | 19 | 20 | 25 | 4 | 5 | ||

5 | 26 | 17 | 14 | 4 | 3.5 | ||

1 | 11 | 24 | 21 | 4.5 | 4 | ||

1 | 22 | 13 | 16 | 3 | 4.5 | ||

4 | 19 | 22 | 18 | 5 | 5 | ||

3.5 | 27 | 20 | 20 | 5 | 2 | ||

1 | 26 | 15 | 15 | 4.5 | 4 | ||

1.5 | 21 | 22 | 26 | 4 | 3 | ||

1.5 | 20 | 22 | 22 | 5 | 4 | ||

2 | 22 | 24 | 16 | 4 | 5 | ||

3.5 | 16 | 26 | 15 | 4 | 4 | ||

4.5 | 22 | 15 | 23 | 4.5 | 5 | ||

1 | 20 | 25 | 28 | 5 | 5 | ||

3.5 | 27 | 20 | 24 | 5 | 5 | ||

3 | 24 | 23 | 16 | 5 | 5 | ||

4 | 26 | 25 | 20 | 3.5 | 4 | ||

5 | 24 | 15 | 16 | 5 | 4 | ||

1 | 16 | 22 | 20 | 4 | 5 | ||

1 | 13 | 22 | 15 | 4.5 | 3 | ||

4.5 | 26 | 19 | 22 | 5 | 4 | ||

1 | 13 | 22 | 25 | 5 | 5 | ||

1 | 14 | 21 | 14 | 3.5 | 5 | ||

2 | 11 | 13 | 23 | 4 | 4.5 | ||

2 | 25 | 20 | 19 | 3.5 | 4 | ||

1.5 | 23 | 28 | 21 | 5 | 4.5 | ||

3.5 | 26 | 20 | 14 | 4.5 | 5 | ||

5 | 26 | 21 | 21 | 5 | 4 | ||

1.5 | 24 | 23 | 15 | 4.5 | 4 | ||

2.5 | 22 | 19 | 16 | 4.5 | 5 | ||

4 | 21 | 14 | 23 | 3.5 | 4.5 | ||

2.5 | 24 | 22 | 20 | 4 | 4.5 | ||

4 | 25 | 13 | 19 | 4.5 | 4 | ||

4.5 | 21 | 22 | 16 | 5 | 4.5 | ||

4 | 28 | 20 | 16 | 5 | 5 | ||

4.5 | 8 | 17 | 15 | 5 | 5 | ||

5 | 12 | 12 | 22 | 4.5 | 5 | ||

5 | 10 | 24 | 10 | 5 | 3.5 | ||

1 | 10 | 22 | 17 | 5 | 5 | ||

1 | 19 | 27 | 19 | 5 | 5 | ||

2.5 | 23 | 17 | 14 | 4.5 | 5 | ||

3 | 23 | 23 | 21 | 3.5 | 5 | ||

3.5 | 25 | 22 | 27 | 5 | 1 | ||

5 | 9 | 21 | 24 | 5 | 4.5 | ||

3 | 21 | 24 | 23 | 5 | 4.5 | ||

4 | 22 | 20 | 17 | 5 | 5 | ||

4.5 | 18 | 26 | 18 | 5 | 4.5 | ||

5 | 24 | 23 | 24 | 5 | 5 | ||

5 | 25 | 21 | 18 | 5 | 5 | ||

4 | 21 | 21 | 10 | 4.5 | 5 | ||

3.5 | 23 | 20 | 18 | 5 | 4 | ||

4.5 | 21 | 18 | 19 | 5 | 5 | ||

2 | 24 | 21 | 12 | 4.5 | 4.5 | ||

4.5 | 20 | 22 | 17 | 5 | 5 | ||

4 | 21 | 17 | 22 | 5 | 5 | ||

4 | 20 | 19 | 23 | 5 | 5 | ||

4 | 12 | 18 | 19 | 5 | 5 | ||

4 | 17 | 24 | 19 | 5 | 5 | ||

4 | 17 | 22 | 26 | 5 | 5 | ||

4.5 | 24 | 22 | 16 | 5 | 5 | ||

5 | 21 | 19 | 18 | 5 | 5 | ||

3 | 13 | 21 | 14 | 4 | 4 | ||

3 | 13 | 22 | 14 | 5 | 5 | ||

5 | 20 | 21 | 24 | 5 | 5 | ||

5 | 22 | 24 | 20 | 5 | 5 | ||

5 | 20 | 16 | 26 | 5 | 4 | ||

5 | 25 | 25 | 24 | 5 | 5 | ||

3.5 | 14 | 16 | 16 | 5 | 5 | ||

4.5 | 15 | 19 | 14 | 5 | 5 | ||

4 | 21 | 24 | 14 | 5 | 5 | ||

4 | 22 | 22 | 16 | 5 | 5 | ||

4.5 | 16 | 24 | 13 | 5 | 5 | ||

5 | 22 | 17 | 20 | 5 | 5 | ||

5 | 18 | 26 | 18 | 5 | 4.5 | ||

2 | 20 | 26 | 5 | ||||

4 | 15 | 16 | 5 | ||||

3 | 26 | 14 | 5 | ||||

4 | 22 | 22 | 5 | ||||

5 | 16 | 13 | 5 | ||||

4 | 15 | 26 | 5 | ||||

4 | 24 | 20 | 5 | ||||

4 | 26 | ||||||

4.5 | 15 | ||||||

5 | 23 | ||||||

5 | 25 | ||||||

5 | 20 | ||||||

5 | 23 | ||||||

3.5 | 25 | ||||||

5 | 15 | ||||||

5 | 28 | ||||||

4 | 22 | ||||||

5 | 24 | ||||||

5 | 16 | ||||||

4 | 20 | ||||||

4 | 16 | ||||||

5 | 20 | ||||||

3 | 15 | ||||||

4.5 | 22 | ||||||

5 | 19 | ||||||

5 | 22 | ||||||

3.5 | 21 | ||||||

4 | 22 | ||||||

5 | 25 | ||||||

5 | 14 | ||||||

4 | 13 | ||||||

4.5 | 23 | ||||||

4 | 19 | ||||||

3.5 | 20 | ||||||

5 | 28 | ||||||

4.5 | 21 | ||||||

5 | 14 | ||||||

4 | 21 | ||||||

4.5 | 20 | ||||||

5 | 21 | ||||||

4.5 | 23 | ||||||

4.5 | 19 | ||||||

3.5 | 14 | ||||||

4 | 22 | ||||||

4.5 | 13 | ||||||

4 | 15 | ||||||

5 | 16 | ||||||

4.5 | 23 | ||||||

4.5 | 20 | ||||||

5 | 22 | ||||||

5 | 20 | ||||||

5 | 17 | ||||||

4 | 19 | ||||||

4.5 | 12 | ||||||

4.5 | 16 | ||||||

5 | 16 | ||||||

5 | 24 | ||||||

5 | 15 | ||||||

5 | 22 | ||||||

5 | 22 | ||||||

3.5 | 10 | ||||||

5 | 27 | ||||||

5 | 17 | ||||||

5 | 19 | ||||||

4.5 | 17 | ||||||

5 | 14 | ||||||

5 | 21 | ||||||

1 | 27 | ||||||

4.5 | 24 | ||||||

3.5 | 23 | ||||||

4.5 | 23 | ||||||

5 | 22 | ||||||

5 | 21 | ||||||

5 | 17 | ||||||

4.5 | 18 | ||||||

5 | 24 | ||||||

5 | 20 | ||||||

5 | 26 | ||||||

5 | 23 | ||||||

5 | 21 | ||||||

4.5 | 21 | ||||||

5 | 24 | ||||||

5 | 18 | ||||||

5 | 10 | ||||||

4 | 18 | ||||||

5 | 19 | ||||||

4.5 | 12 | ||||||

5 | 20 | ||||||

5 | 17 | ||||||

5 | 22 | ||||||

5 | 18 | ||||||

5 | 23 | ||||||

5 | 19 | ||||||

5 | 19 | ||||||

5 | 26 | ||||||

5 | 16 | ||||||

5 | 18 | ||||||

4.5 | 21 | ||||||

5 | 22 | ||||||

4 | 14 | ||||||

5 | 17 | ||||||

5 | 14 | ||||||

5 | 19 | ||||||

5 | 18 | ||||||

5 | 24 | ||||||

5 | 24 | ||||||

5 | 22 | ||||||

5 | 20 | ||||||

4 | 26 | ||||||

5 | 24 | ||||||

5 | 16 | ||||||

5 | 14 | ||||||

5 | 14 | ||||||

5 | 16 | ||||||

5 | 22 | ||||||

5 | 19 | ||||||

5 | 13 | ||||||

4 | 21 | ||||||

5 | 20 | ||||||

5 | 22 | ||||||

5 | 21 | ||||||

5 | 24 | ||||||

4.5 | 18 | ||||||

5 | 16 | ||||||

5 | 25 | ||||||

5 | 26 | ||||||

5 | 16 | ||||||

5 | 14 | ||||||

5 | 16 | ||||||

5 | 19 | ||||||

5 | 24 | ||||||

5 | 22 | ||||||

5 | 22 | ||||||

5 | 24 | ||||||

5 | 13 | ||||||

5 | 26 | ||||||

5 | 17 | ||||||

5 | 26 | ||||||

5 | 20 | ||||||

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Last Updated on September 14, 2019 by EssayPro