MM207 Unit 6: Confidence Intervals for Means and Population Proportions
Discusses confidence intervals and their application in statistics.
Hannah Perez
Contributor
4.7
51
3 days ago
Preview (2 of 2)
Sign in to access the full document!
MM207 Unit 6 Chapter 6 Project
ROBYN GALINDO
1
MM207 Unit 6: Confidence Intervals for Means and Population
Proportions
Total points are 40. Points are included with each problem.
Included with each section or problem are reference examples and end of section
exercises that can be used as a guide. Be sure to show your work in case partial
credit is awarded. To receive full credit, work must be shown if applicable.
Section 6.1: Confidence Intervals for the Mean (Large Samples)
1. Find the critical value zc necessary to form a confidence interval at the given
level of confidence. (References: definition for level of confidence page
311, end of section exercises 5 – 8 page 317) (2.5 points each)
a. 90%
½ (1-.90) = 0.05 = 1.645
b. 80%
½ (1-.80) = 0.10 = 1.28
2. The new Twinkle bulb has a standard deviation 35
hours. A random
sample of 50 light bulbs is selected from inventory. The sample mean was
found to be X 550 hours.
a. Find the margin of error E for a 90% confidence interval. (5 points)
Round your answer to the nearest hundredths. . (References:
definition of margin of error on page 312 and example 2 on
page 312).
E = 1.645 (35/√50) = 8.14
b. Construct a 90% confidence interval for the mean life, of all Twinkle
bulbs. (5 points) (References: example 5 page 315, end of
section exercises 51 - 56 pages 319 - 320)
Left Endpoint: 550 – 8.14 = 541.86
Right Endpoint: 550 + 8.14 = 558.14
541.86 < μ < 558.14
3. A standard placement test has a mean of 115 and a standard deviation of
= 10. Determine the minimum sample size if we want to be 90% certain
that we are within 2 points of the true mean. (References: example 6
page 316, end of section exercises 58 - 62 pages 321 - 322)
(5 points)
n = (1.645)(10)² = 271
Section 6.2: Confidence Intervals for the Mean (Small Samples)
ROBYN GALINDO
1
MM207 Unit 6: Confidence Intervals for Means and Population
Proportions
Total points are 40. Points are included with each problem.
Included with each section or problem are reference examples and end of section
exercises that can be used as a guide. Be sure to show your work in case partial
credit is awarded. To receive full credit, work must be shown if applicable.
Section 6.1: Confidence Intervals for the Mean (Large Samples)
1. Find the critical value zc necessary to form a confidence interval at the given
level of confidence. (References: definition for level of confidence page
311, end of section exercises 5 – 8 page 317) (2.5 points each)
a. 90%
½ (1-.90) = 0.05 = 1.645
b. 80%
½ (1-.80) = 0.10 = 1.28
2. The new Twinkle bulb has a standard deviation 35
hours. A random
sample of 50 light bulbs is selected from inventory. The sample mean was
found to be X 550 hours.
a. Find the margin of error E for a 90% confidence interval. (5 points)
Round your answer to the nearest hundredths. . (References:
definition of margin of error on page 312 and example 2 on
page 312).
E = 1.645 (35/√50) = 8.14
b. Construct a 90% confidence interval for the mean life, of all Twinkle
bulbs. (5 points) (References: example 5 page 315, end of
section exercises 51 - 56 pages 319 - 320)
Left Endpoint: 550 – 8.14 = 541.86
Right Endpoint: 550 + 8.14 = 558.14
541.86 < μ < 558.14
3. A standard placement test has a mean of 115 and a standard deviation of
= 10. Determine the minimum sample size if we want to be 90% certain
that we are within 2 points of the true mean. (References: example 6
page 316, end of section exercises 58 - 62 pages 321 - 322)
(5 points)
n = (1.645)(10)² = 271
Section 6.2: Confidence Intervals for the Mean (Small Samples)
Preview Mode
Sign in to access the full document!
100%
Study Now!
XY-Copilot AI
Unlimited Access
Secure Payment
Instant Access
24/7 Support
Document Chat
Document Details
University
Kaplan University School of Business and Management
Subject
Mathematics