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) Customer ID Overall Website Satisfaction Easy to Navigate Ease of Ordering Satisfaction with Customer Service Likely to Recommend to a Friend Likely to Purchase Again 5001 2 1 3 4 2 N 5002 4 3 3 5 3 Y 5003 2 2 3 3 3 N 5004 3 1 1 4 2 Y 5005 5 4 3 5 4 N 5006 1 2 3 5 3 N 5007 4 3 3 4 4 N 5008 3 2 1 3 3 N 5009 2 3 2 2 2 Y 5010 2 2 2 4 2 Y 5011 3 3 2 2 4 Y 5012 2 2 2 4 2 Y 5013 4 3 5 5 4 Y 5014 3 3 4 2 3 Y 5015 3 3 1 3 4 N 5016 1 3 2 2 5 Y 5017 2 1 2 5 2 N 5018 4 4 4 4 3 N 5019 1 2 1 3 5 N 5020 5 4 3 5 4 Y 5021 3 1 2 2 3 N 5022 4 3 3 5 5 Y 5023 2 4 3 3 4 N 5024 3 3 1 4 4 N 5025 2 2 1 3 3 N 5026 2 1 3 2 3 Y 5027 1 1 1 2 3 N 5028 2 2 2 2 3 N 5029 1 3 2 1 4 Y 5030 4 2 4 3 5 N 5031 4 3 3 4 3 Y 5032 3 4 2 3 3 N 5033 5 5 2 4 5 Y 5034 3 3 3 3 2 N 5035 2 3 3 3 2 N 5036 4 4 3 5 3 N 5037 4 2 2 4 4 N 5038 1 1 2 4 2 N 5039 5 5 3 4 4 Y 5040 5 1 4 3 2 Y 5041 4 4 4 5 4 Y 5042 3 1 2 5 2 N 5043 5 4 2 3 5 N 5044 3 4 3 1 4 N 5045 4 2 3 4 4 N 5046 3 5 3 4 4 Y 5047 4 5 2 5 4 Y 5048 5 3 3 5 5 Y 5049 2 5 2 2 2 Y 5050 3 4 2 2 3 N 5051 2 2 5 2 2 N 5052 3 4 3 2 2 N 5053 4 4 4 3 3 N 5054 2 4 1 3 3 N 5055 2 1 2 1 3 N 5056 4 3 2 3 3 N 5057 3 3 3 4 4 Y 5058 2 3 3 3 2 Y 5059 3 2 3 4 4 N 5060 5 4 4 5 3 N 5061 2 1 2 4 3 Y 5062 4 3 2 3 3 Y 5063 5 5 4 4 1 N 5064 2 2 1 4 3 N 5065 2 1 2 2 4 Y 5066 2 2 3 3 4 N 5067 3 4 3 2 3 N 5068 2 2 2 2 3 Y 5069 5 5 2 4 3 N 5070 3 2 2 5 2 N 5071 4 4 5 5 3 Y 5072 4 1 4 3 4 N 5073 3 3 2 4 4 N 5074 3 5 2 3 3 N 5075 2 3 3 4 2 N 5076 1 2 1 5 1 N 5077 3 5 2 2 2 Y 5078 1 1 3 3 3 N 5079 4 3 2 4 5 Y 5080 3 3 4 2 3 Y 5081 4 4 3 3 3 Y 5082 2 3 2 3 2 N 5083 5 5 2 5 1 Y 5084 3 3 2 4 3 Y 5085 5 3 2 5 5 Y 5086 5 4 3 5 3 Y 5087 3 3 3 5 3 Y 5088 4 3 4 2 4 N 5089 1 1 3 4 1 N 5090 5 5 3 5 2 Y 5091 4 3 4 4 4 N 5092 4 2 4 4 2 N 5093 2 3 3 3 2 N 5094 3 4 3 3 3 Y 5095 3 4 4 5 3 Y 5096 4 3 3 3 3 Y 5097 3 4 2 3 3 Y 5098 2 4 1 3 3 N 5099 2 2 1 1 3 Y 5100 4 4 3 2 4 N 3.08 2.95 2.61 3.44 3.13 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). Rewrite these new confidence intervals in the form , where is the sample mean for each variable and is the margin of error. 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!
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) Customer ID Overall Website Satisfaction Easy to Navigate Ease of Ordering Satisfaction with Customer Service Likely to Recommend to a Friend Likely to Purchase Again 5001 2 1 3 4 2 N 5002 4 3 3 5 3 Y 5003 2 2 3 3 3 N 5004 3 1 1 4 2 Y 5005 5 4 3 5 4 N 5006 1 2 3 5 3 N 5007 4 3 3 4 4 N 5008 3 2 1 3 3 N 5009 2 3 2 2 2 Y 5010 2 2 2 4 2 Y 5011 3 3 2 2 4 Y 5012 2 2 2 4 2 Y 5013 4 3 5 5 4 Y 5014 3 3 4 2 3 Y 5015 3 3 1 3 4 N 5016 1 3 2 2 5 Y 5017 2 1 2 5 2 N 5018 4 4 4 4 3 N 5019 1 2 1 3 5 N 5020 5 4 3 5 4 Y 5021 3 1 2 2 3 N 5022 4 3 3 5 5 Y 5023 2 4 3 3 4 N 5024 3 3 1 4 4 N 5025 2 2 1 3 3 N 5026 2 1 3 2 3 Y 5027 1 1 1 2 3 N 5028 2 2 2 2 3 N 5029 1 3 2 1 4 Y 5030 4 2 4 3 5 N 5031 4 3 3 4 3 Y 5032 3 4 2 3 3 N 5033 5 5 2 4 5 Y 5034 3 3 3 3 2 N 5035 2 3 3 3 2 N 5036 4 4 3 5 3 N 5037 4 2 2 4 4 N 5038 1 1 2 4 2 N 5039 5 5 3 4 4 Y 5040 5 1 4 3 2 Y 5041 4 4 4 5 4 Y 5042 3 1 2 5 2 N 5043 5 4 2 3 5 N 5044 3 4 3 1 4 N 5045 4 2 3 4 4 N 5046 3 5 3 4 4 Y 5047 4 5 2 5 4 Y 5048 5 3 3 5 5 Y 5049 2 5 2 2 2 Y 5050 3 4 2 2 3 N 5051 2 2 5 2 2 N 5052 3 4 3 2 2 N 5053 4 4 4 3 3 N 5054 2 4 1 3 3 N 5055 2 1 2 1 3 N 5056 4 3 2 3 3 N 5057 3 3 3 4 4 Y 5058 2 3 3 3 2 Y 5059 3 2 3 4 4 N 5060 5 4 4 5 3 N 5061 2 1 2 4 3 Y 5062 4 3 2 3 3 Y 5063 5 5 4 4 1 N 5064 2 2 1 4 3 N 5065 2 1 2 2 4 Y 5066 2 2 3 3 4 N 5067 3 4 3 2 3 N 5068 2 2 2 2 3 Y 5069 5 5 2 4 3 N 5070 3 2 2 5 2 N 5071 4 4 5 5 3 Y 5072 4 1 4 3 4 N 5073 3 3 2 4 4 N 5074 3 5 2 3 3 N 5075 2 3 3 4 2 N 5076 1 2 1 5 1 N 5077 3 5 2 2 2 Y 5078 1 1 3 3 3 N 5079 4 3 2 4 5 Y 5080 3 3 4 2 3 Y 5081 4 4 3 3 3 Y 5082 2 3 2 3 2 N 5083 5 5 2 5 1 Y 5084 3 3 2 4 3 Y 5085 5 3 2 5 5 Y 5086 5 4 3 5 3 Y 5087 3 3 3 5 3 Y 5088 4 3 4 2 4 N 5089 1 1 3 4 1 N 5090 5 5 3 5 2 Y 5091 4 3 4 4 4 N 5092 4 2 4 4 2 N 5093 2 3 3 3 2 N 5094 3 4 3 3 3 Y 5095 3 4 4 5 3 Y 5096 4 3 3 3 3 Y 5097 3 4 2 3 3 Y 5098 2 4 1 3 3 N 5099 2 2 1 1 3 Y 5100 4 4 3 2 4 N 3.08 2.95 2.61 3.44 3.13 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). Rewrite these new confidence intervals in the form , where is the sample mean for each variable and is the margin of error. 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!
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
Related questions
Question
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)
| Customer ID | Overall Website Satisfaction | Easy to Navigate | Ease of Ordering | Satisfaction with Customer Service | Likely to Recommend to a Friend | Likely to Purchase Again |
| 5001 | 2 | 1 | 3 | 4 | 2 | N |
| 5002 | 4 | 3 | 3 | 5 | 3 | Y |
| 5003 | 2 | 2 | 3 | 3 | 3 | N |
| 5004 | 3 | 1 | 1 | 4 | 2 | Y |
| 5005 | 5 | 4 | 3 | 5 | 4 | N |
| 5006 | 1 | 2 | 3 | 5 | 3 | N |
| 5007 | 4 | 3 | 3 | 4 | 4 | N |
| 5008 | 3 | 2 | 1 | 3 | 3 | N |
| 5009 | 2 | 3 | 2 | 2 | 2 | Y |
| 5010 | 2 | 2 | 2 | 4 | 2 | Y |
| 5011 | 3 | 3 | 2 | 2 | 4 | Y |
| 5012 | 2 | 2 | 2 | 4 | 2 | Y |
| 5013 | 4 | 3 | 5 | 5 | 4 | Y |
| 5014 | 3 | 3 | 4 | 2 | 3 | Y |
| 5015 | 3 | 3 | 1 | 3 | 4 | N |
| 5016 | 1 | 3 | 2 | 2 | 5 | Y |
| 5017 | 2 | 1 | 2 | 5 | 2 | N |
| 5018 | 4 | 4 | 4 | 4 | 3 | N |
| 5019 | 1 | 2 | 1 | 3 | 5 | N |
| 5020 | 5 | 4 | 3 | 5 | 4 | Y |
| 5021 | 3 | 1 | 2 | 2 | 3 | N |
| 5022 | 4 | 3 | 3 | 5 | 5 | Y |
| 5023 | 2 | 4 | 3 | 3 | 4 | N |
| 5024 | 3 | 3 | 1 | 4 | 4 | N |
| 5025 | 2 | 2 | 1 | 3 | 3 | N |
| 5026 | 2 | 1 | 3 | 2 | 3 | Y |
| 5027 | 1 | 1 | 1 | 2 | 3 | N |
| 5028 | 2 | 2 | 2 | 2 | 3 | N |
| 5029 | 1 | 3 | 2 | 1 | 4 | Y |
| 5030 | 4 | 2 | 4 | 3 | 5 | N |
| 5031 | 4 | 3 | 3 | 4 | 3 | Y |
| 5032 | 3 | 4 | 2 | 3 | 3 | N |
| 5033 | 5 | 5 | 2 | 4 | 5 | Y |
| 5034 | 3 | 3 | 3 | 3 | 2 | N |
| 5035 | 2 | 3 | 3 | 3 | 2 | N |
| 5036 | 4 | 4 | 3 | 5 | 3 | N |
| 5037 | 4 | 2 | 2 | 4 | 4 | N |
| 5038 | 1 | 1 | 2 | 4 | 2 | N |
| 5039 | 5 | 5 | 3 | 4 | 4 | Y |
| 5040 | 5 | 1 | 4 | 3 | 2 | Y |
| 5041 | 4 | 4 | 4 | 5 | 4 | Y |
| 5042 | 3 | 1 | 2 | 5 | 2 | N |
| 5043 | 5 | 4 | 2 | 3 | 5 | N |
| 5044 | 3 | 4 | 3 | 1 | 4 | N |
| 5045 | 4 | 2 | 3 | 4 | 4 | N |
| 5046 | 3 | 5 | 3 | 4 | 4 | Y |
| 5047 | 4 | 5 | 2 | 5 | 4 | Y |
| 5048 | 5 | 3 | 3 | 5 | 5 | Y |
| 5049 | 2 | 5 | 2 | 2 | 2 | Y |
| 5050 | 3 | 4 | 2 | 2 | 3 | N |
| 5051 | 2 | 2 | 5 | 2 | 2 | N |
| 5052 | 3 | 4 | 3 | 2 | 2 | N |
| 5053 | 4 | 4 | 4 | 3 | 3 | N |
| 5054 | 2 | 4 | 1 | 3 | 3 | N |
| 5055 | 2 | 1 | 2 | 1 | 3 | N |
| 5056 | 4 | 3 | 2 | 3 | 3 | N |
| 5057 | 3 | 3 | 3 | 4 | 4 | Y |
| 5058 | 2 | 3 | 3 | 3 | 2 | Y |
| 5059 | 3 | 2 | 3 | 4 | 4 | N |
| 5060 | 5 | 4 | 4 | 5 | 3 | N |
| 5061 | 2 | 1 | 2 | 4 | 3 | Y |
| 5062 | 4 | 3 | 2 | 3 | 3 | Y |
| 5063 | 5 | 5 | 4 | 4 | 1 | N |
| 5064 | 2 | 2 | 1 | 4 | 3 | N |
| 5065 | 2 | 1 | 2 | 2 | 4 | Y |
| 5066 | 2 | 2 | 3 | 3 | 4 | N |
| 5067 | 3 | 4 | 3 | 2 | 3 | N |
| 5068 | 2 | 2 | 2 | 2 | 3 | Y |
| 5069 | 5 | 5 | 2 | 4 | 3 | N |
| 5070 | 3 | 2 | 2 | 5 | 2 | N |
| 5071 | 4 | 4 | 5 | 5 | 3 | Y |
| 5072 | 4 | 1 | 4 | 3 | 4 | N |
| 5073 | 3 | 3 | 2 | 4 | 4 | N |
| 5074 | 3 | 5 | 2 | 3 | 3 | N |
| 5075 | 2 | 3 | 3 | 4 | 2 | N |
| 5076 | 1 | 2 | 1 | 5 | 1 | N |
| 5077 | 3 | 5 | 2 | 2 | 2 | Y |
| 5078 | 1 | 1 | 3 | 3 | 3 | N |
| 5079 | 4 | 3 | 2 | 4 | 5 | Y |
| 5080 | 3 | 3 | 4 | 2 | 3 | Y |
| 5081 | 4 | 4 | 3 | 3 | 3 | Y |
| 5082 | 2 | 3 | 2 | 3 | 2 | N |
| 5083 | 5 | 5 | 2 | 5 | 1 | Y |
| 5084 | 3 | 3 | 2 | 4 | 3 | Y |
| 5085 | 5 | 3 | 2 | 5 | 5 | Y |
| 5086 | 5 | 4 | 3 | 5 | 3 | Y |
| 5087 | 3 | 3 | 3 | 5 | 3 | Y |
| 5088 | 4 | 3 | 4 | 2 | 4 | N |
| 5089 | 1 | 1 | 3 | 4 | 1 | N |
| 5090 | 5 | 5 | 3 | 5 | 2 | Y |
| 5091 | 4 | 3 | 4 | 4 | 4 | N |
| 5092 | 4 | 2 | 4 | 4 | 2 | N |
| 5093 | 2 | 3 | 3 | 3 | 2 | N |
| 5094 | 3 | 4 | 3 | 3 | 3 | Y |
| 5095 | 3 | 4 | 4 | 5 | 3 | Y |
| 5096 | 4 | 3 | 3 | 3 | 3 | Y |
| 5097 | 3 | 4 | 2 | 3 | 3 | Y |
| 5098 | 2 | 4 | 1 | 3 | 3 | N |
| 5099 | 2 | 2 | 1 | 1 | 3 | Y |
| 5100 | 4 | 4 | 3 | 2 | 4 | N |
| 3.08 | 2.95 | 2.61 | 3.44 | 3.13 |
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). Rewrite these new confidence intervals in the form , where is the sample mean for each variable and is the margin of error. 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!
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