The margin of error is determined by the standard deviation, the desired confidence level, and the sample size. Suppose a project director conducted a survey of the daily rental costs for medium-size automobiles and found that a mean daily rental cost of $55.00. Based on a previous study, the director also knew that a reasonable planning value for the population standard deviation was $9.65. The graph below shows a 95% confidence interval using 9.65 as the planning value of the standard deviation. Move the slider slowly from left to right to see how the margin of error changes as n changes.
The margin of error is determined by the standard deviation, the desired confidence level, and the sample size. Suppose a project director conducted a survey of the daily rental costs for medium-size automobiles and found that a mean daily rental cost of $55.00. Based on a previous study, the director also knew that a reasonable planning value for the population standard deviation was $9.65. The graph below shows a 95% confidence interval using 9.65 as the planning value of the standard deviation. Move the slider slowly from left to right to see how the margin of error changes as n changes.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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The margin of error is determined by the standard deviation, the desired confidence level, and the
Suppose a project director conducted a survey of the daily rental costs for medium-size automobiles and found that a mean daily rental cost of $55.00. Based on a previous study, the director also knew that a reasonable planning value for the population standard deviation was $9.65.
The graph below shows a 95% confidence interval using 9.65 as the planning value of the standard deviation. Move the slider slowly from left to right to see how the margin of error changes as n changes.
![44
n = 5
46
95% Confidence Interval: [43.02, 66.98]
48
50
52
54
50
56
58
60
Created by Gary H. McClelland, Professor Emeritus | University of Colorado Boulder
ⒸCengage Learning. All Rights Reserved.
1. As the sample size is increased from n =18 to n = 28, what is the difference in the margin of error for those two sample sizes?
a. 1.06
b. 3.74
c. 4.8
d. 5.96
-Select-
a. The confidence interval width changes at the same rate across all sample sizes.
b. The confidence interval width changes rapidly at smaller sample sizes and slowly at larger sample sizes.
c. The confidence interval width changes slowly at smaller sample sizes and rapidly at larger sample sizes.
-Select- ✓
62
64
100
66
2. Move the slider slowly back and forth several time across the entire sample size range. Note the rate at which the interval changes at smaller sample sizes versus larger sample sizes for a given confidence
level (in this case 95%). What is happening?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e31a6bb-45a4-4b1f-bf71-c8ce1df7af01%2F5957f5f5-75c0-4cc7-86e4-4f2f7b9363ea%2Fynjj5j_processed.png&w=3840&q=75)
Transcribed Image Text:44
n = 5
46
95% Confidence Interval: [43.02, 66.98]
48
50
52
54
50
56
58
60
Created by Gary H. McClelland, Professor Emeritus | University of Colorado Boulder
ⒸCengage Learning. All Rights Reserved.
1. As the sample size is increased from n =18 to n = 28, what is the difference in the margin of error for those two sample sizes?
a. 1.06
b. 3.74
c. 4.8
d. 5.96
-Select-
a. The confidence interval width changes at the same rate across all sample sizes.
b. The confidence interval width changes rapidly at smaller sample sizes and slowly at larger sample sizes.
c. The confidence interval width changes slowly at smaller sample sizes and rapidly at larger sample sizes.
-Select- ✓
62
64
100
66
2. Move the slider slowly back and forth several time across the entire sample size range. Note the rate at which the interval changes at smaller sample sizes versus larger sample sizes for a given confidence
level (in this case 95%). What is happening?
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