MATH 280 FU Statistics Website Satisfaction Scores Data Questions

Franklin UniversityMath 280 – Introduction to Probability and Statistics
Name: _____________________
Module 6 Application Assignment (16 Points)
This assignment has 50 points in total. Your percent score out of 50 points will be multiplied
by 16 to find your assignment score.
WEBSITE SATISFACTION SCORES
You are a webmaster and senior marketing analyst for a local clothing manufacturer experiencing recent
growth in their business. Led by your efforts, your company recently completed a web redesign
including a new system where customers can create and order custom designs online. To evaluate your
customers’ satisfaction with the new website, you’ve surveyed a random sampling of 100 recent
customers and asked them to rate their satisfaction on a scale from 1-5 (5 being the highest) on the
following dimensions:
•
•
•
•
•
•
Overall satisfaction with your company website
Ease of navigation of the website
Ease of ordering on the website
Satisfaction with your company’s customer service
Their likelihood to recommend your company to a friend
If they are likely to purchase from your company again in the future (Yes/No)
Answer the following questions about the website satisfaction data you’ve collected:
1. (5 pts) Calculate and display the average scores and standard deviation for the five variables scored
on the 1-5 scale above: Overall satisfaction, Ease of Navigation, Ease of Ordering, Satisfaction with
Customer Service, and Likelihood to Recommend.
2. (3 pts) Which area represents the biggest opportunity for improvement, and seems to be the biggest
challenge with the new website? Why did you choose that area?
3. (3 pts) Which area seems to be your company’s strongest area? How do you know?
4. (6 pts) Calculate and display the 90% confidence intervals for the five satisfaction variables above:
Overall satisfaction, Ease of Navigation, Ease of Ordering, Satisfaction with Customer Service, and
Likelihood to Recommend. Write these in interval notation: (lower limit, upper limit)
5. (5 pts) Rewrite these five confidence intervals in the form 𝑥̅ ± 𝑚, where 𝑥̅ is the sample mean for
each variable and 𝑚 is the margin of error.
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081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: _____________________
6. (6 pts) Now calculate and display the 95% confidence intervals for the five satisfaction variables
above: Overall satisfaction, Ease of Navigation, Ease of Ordering, Satisfaction with Customer Service,
and Likelihood to Recommend. Write these in interval notation: (lower limit, upper limit)
7. (5 pts) Rewrite these new confidence intervals in the form 𝑥̅ ± 𝑚, where 𝑥̅ is the sample mean for
each variable and 𝑚 is the margin of error.
8. (5 pts) Suppose you wanted to decrease the margin of error on your Overall Website Satisfaction
metric to 0.1. Assuming that the sample standard deviation for this score and the confidence level
stayed the same, what sample size would be needed to achieve this lower margin of error? Show
your work!
9. (6 pts) Calculate and display the 90% confidence intervals for the five satisfaction variables above:
Overall satisfaction, Ease of Navigation, Ease of Ordering, Satisfaction with Customer Service, and
Likelihood to Recommend. Write these in interval notation: (lower limit, upper limit) for those
customers who say they are likely to purchase from you again.
10. (6 pts) Calculate and display the 90% confidence intervals for the five satisfaction variables above:
Overall satisfaction, Ease of Navigation, Ease of Ordering, Satisfaction with Customer Service, and
Likelihood to Recommend. Write these in interval notation: (lower limit, upper limit) for those
customers who say they are NOT likely to purchase from you again.
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Customer ID Overall Website Satisfaction
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
Easy to Navigate
2
4
2
3
5
1
4
3
2
2
3
2
4
3
3
1
2
4
1
5
3
4
2
3
2
2
1
2
1
4
4
3
5
3
2
4
4
1
5
5
4
3
5
3
4
3
Ease of Ordering
1
3
2
1
4
2
3
2
3
2
3
2
3
3
3
3
1
4
2
4
1
3
4
3
2
1
1
2
3
2
3
4
5
3
3
4
2
1
5
1
4
1
4
4
2
5
3
3
3
1
3
3
3
1
2
2
2
2
5
4
1
2
2
4
1
3
2
3
3
1
1
3
1
2
2
4
3
2
2
3
3
3
2
2
3
4
4
2
2
3
3
3
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
4
5
2
3
2
3
4
2
2
4
3
2
3
5
2
4
5
2
2
2
3
2
5
3
4
4
3
3
2
1
3
1
4
3
4
2
5
3
5
5
3
4
1
5
4
4
2
5
3
5
4
2
4
4
4
1
3
3
3
2
4
1
3
5
2
1
2
4
2
5
2
4
1
3
5
3
2
5
1
3
3
4
3
5
3
3
4
3
3
1
5
3
2
3
2
3
2
2
5
3
4
1
2
2
3
3
3
4
2
2
4
1
2
3
3
2
2
2
5
4
2
2
3
1
2
3
2
4
3
2
2
2
2
3
3
4
3
3
4
4
3
5094
5095
5096
5097
5098
5099
5100
3
3
4
3
2
2
4
4
4
3
4
4
2
4
3
4
3
2
1
1
3
Satisfaction with Customer Service
Likely to Recommend to a Friend
4
5
3
4
5
5
4
3
2
4
2
4
5
2
3
2
5
4
3
5
2
5
3
4
3
2
2
2
1
3
4
3
4
3
3
5
4
4
4
3
5
5
3
1
4
4
2
3
3
2
4
3
4
3
2
2
4
2
4
3
4
5
2
3
5
4
3
5
4
4
3
3
3
3
4
5
3
3
5
2
2
3
4
2
4
2
4
2
5
4
4
4
Likely to Purchase Again
N
Y
N
Y
N
N
N
N
Y
Y
Y
Y
Y
Y
N
Y
N
N
N
Y
N
Y
N
N
N
Y
N
N
Y
N
Y
N
Y
N
N
N
N
N
Y
Y
Y
N
N
N
N
Y
5
5
2
2
2
2
3
3
1
3
4
3
4
5
4
3
4
4
2
3
2
2
4
5
5
3
4
3
4
5
2
3
4
2
3
3
5
4
5
5
5
2
4
5
4
4
3
4
5
2
3
2
2
3
3
3
3
4
2
4
3
3
3
1
3
4
4
3
3
3
2
3
4
4
3
2
1
2
3
5
3
3
2
1
3
5
3
3
4
1
2
4
2
2
Y
Y
Y
N
N
N
N
N
N
N
Y
Y
N
N
Y
Y
N
N
Y
N
N
Y
N
N
Y
N
N
N
N
N
Y
N
Y
Y
Y
N
Y
Y
Y
Y
Y
N
N
Y
N
N
N
3
5
3
3
3
1
2
3
3
3
3
3
3
4
Y
Y
Y
Y
N
Y
N