HW3_STAT302
docx
keyboard_arrow_up
School
American University *
*We aren’t endorsed by this school
Course
302
Subject
Statistics
Date
Jan 9, 2024
Type
docx
Pages
2
Uploaded by DeaconMoonPorcupine36
HW3: Due
Thursday Feb 17 via blackboard
100 points
Find Z* and T* critical values (10 points)
What is the Zcritical value for a confidence interval with C = 0.9?
1.2815516
What is the Tcritical value for a confidence interval with C = 0.9 and sample size = 15
0.80882893
What is the Tcritical value for a confidence interval with C = 0.9 and sample size= 100?
0.81485876
What happens to the Tcritical value (assuming confidence level stays the same) when you increase the
sample size?
The Tcritical value also increases.
Estimating the sample size (30 points)
Let’s assume that you want to estimate the sample size for a survey of American University students to
determine their mean height.
What is the sample size of your random sample to achieve a margin of
error = 0.25 inches at a confidence level = 0.95? Assume that the population standard deviation is 2.5
inches.
1537
Confidence Interval for a population mean (30)
In ER of a hospital, a patient was taken 7 consecutive blood pressure measurements at random.
Assume
that the measurements are normally distributed.
Form a confidence interval for the true blood pressure
of the patient when the sample mean blood pressure is 135 and the sample standard deviation is 10.
Confidence level is 0.90
a)
What is the T-critical value corresponding to C = 0.9 and n = 7?
a.
1.4149239
b)
What is the standard error?
a.
10/sqrt(135) = 0.86
c)
What is the margin of error?
a.
2.8313292
d)
What is the confidence interval?
a.
0.9
Confidence Interval for a population proportion (30 points):
Three independently taken recent polls of likely voters were asked if they would vote for Biden.
Poll nr 1: sample size = 500, sample proportion = 52 %
Poll nr 2: sample size = 1000, sample proportion = 50 %
Poll nr 3: sample size = 2500, sample proportion = 48%
a.
Build a 95% confidence interval for the proportion of all likely voters who would vote for Biden in
a general election for poll nr1, poll nr. 2 and poll nr3.
a.
Margin errors:
i.
Poll nr1 = 0.087582104
ii.
Poll nr2 = 0.061979503
iii.
Poll nr3 = 0.039167908
b.
Compare and comment on their margins of error!
a.
Poll nr1 has the largest margin or error, while poll nr3 has the lowest. I tried testing poll
nr1 with sample proportion of 48% and I still got a similar (if not same) margin of error.
This shows that the margin of error inversely proportional to the sample size. The larger
the sample size is, the smaller the margin of error is.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Documents
Related Questions
total plasma volume is important in determining the required plasma component in blood replacement therapy for personal growth and surgery plasma volume is influenced by the overall health and physical activity of an individual suppose that a random sample 40 mile firefighters are tested in that they have a plasma volume sample mean of x=37.5 ml/kg assume thqy o=7.70 ml/kg for the distribution of blood plasma. Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? Lower limit? Upper limit? (Round your answers to two decimal places)
arrow_forward
What critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 21 observations?
Find the t-table here.
t* = 1.721
t* = 1.725
t* = 2.080
t* = 2.086
arrow_forward
Create a confidence interval for a population proportion for a point estimate of 0.6 with a margin of error equal to $0.06.
(
,
)
[three decimal accuracy]
[three decimal accuracy]
Determine the z-scores corresponding to a 90% confidence interval.
negative z-score =
[three decimal accuracy]
positive z-score =
[three decimal accuracy]
arrow_forward
How do you solve these problems?
arrow_forward
total plasma volume is important in determining the required plasma component in blood replacement therapy for personal growth and surgery plasma volume is influenced by the overall health and physical activity of an individual suppose that a random sample 50 male firefighters are tested in that they have a plasma volume sample mean of x=37.5 ml/kg assume thqy o=7.20 ml/kg for the distribution of blood plasma
A) when finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.)
B) find the sample size necessary for a 99% confidence level with maximal margin of error E= 2.10 for the mean plasma volume in male firefighters round to nearest whole number
arrow_forward
Create a 95% confidence interval for the population proportion of Orange candies. sample size is 30, point estimate is 0.44, critical z value is 0.152. Standard error is 0.602. Margin of error is 0.017
what is the lower bound and upper bound and interpretation?
arrow_forward
APA Format - Google Docs
entral
X
e.com/courses/84804/assignments/2104292?module_item_id=5433041
ect Zoom
Home Page - InSite
You can retry this question below
A poll of 2816 U.S. adults found that 1522 U.S. adults, or 54.048% regularly used Facebook as a news
source.
Find the margin of error and confidence interval for the percentage of U.S. adults who regularly use
Facebook as a news source, at the 90% level of confidence. Express all answers as percentages rounded to
2 decimal places. Do not write the percent sign.
Margin of Error (as a percentage): 1.65
Confidence Interval: 52.40
Margin of Error (as a percentage): 1.96
Confidence Interval: 51.85
X% to 55.70
Margin of Error (as a percentage): 2.58
Confidence Interval: 50.47
Now find the margin of error and confidence interval for the percentage of U.S. adults who regularly use
Facebook as a news source, at the 95% level of confidence.
X% to 56.22
Section 9.2 and 9.3 Homework E X
X
to 57.61
X
X%
Finally, find the margin of error and…
arrow_forward
I need help with this one please thank you. I need you to find the P-value, and to construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.
arrow_forward
How do I find the critical value using statcrunch and manually in a calculator for this problem?
Find the critical value Zα/2 that corresponds to the given confidence level.
98%
arrow_forward
Hua Nick - Final.Exam.pdf
270%
7. The standard deviation for a large population
is 3. A simple random sample is taken from
this population, and this sample is used to
calculate a 96% confidence interval for the
population mean. If this confidence interval
has a margin of error of 0.283, what is the
sample size?
(A)
3
(В) 112
(C) 344
(D) 432
(E) 474
立
arrow_forward
Find the critical value
tc
for the confidence level
c=0.90
and sample size
n=13.
tc=
(Round to the nearest thousandth as nee
arrow_forward
P(T<=t) one-tail 0.000000525
P(T<=t) two-tail 0.0000001005
1. What is the standard error for the difference between two means? 2. Compute the test statistic3. Apply the rejection rule using the critical value approach 4. Develop a99% confidence interval of the difference between the mean annual cost of attending private and public colleges.
arrow_forward
Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces. A random sample of 24 AAA batteries produced by this manufacturer lasted a mean of 10.8 hours with a standard deviation of 1.6 hours. Find a 95% confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer. Then give its lower limit and upper limit.
arrow_forward
Confidence Intervals
5.) Listed below are the measured radiation emissions (in W/kg) for a number of cell phonesfrom a variety of carriers, based on data from the Environmental Working Group. The mediaoften present reports of the dangers of cell phone radiation as a potential cause of cancer.Construct a 90% confidence interval estimate of the population mean based on this sample.0.38 0.55 1.54 1.55 0.50 0.60 0.92 0.96 1.00 0.86 1.46What does the result suggest about the Federal Communications Standard that cell phoneradiation must be 1.6 W/kg or less?
arrow_forward
Lifetime of electronics: In a simple random sample of 100 electronic components produced by a certain method, the mean
lifetime was 125 hours. Assume that component llfetimes are normally distributed with population standard deviation o
= 20
hours. Round the critical value to no less than three decimal places.
arrow_forward
Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was m = 15.1. A sample of n = 16 of today’s children produces a mean score of M = 23.3 with SS = 240.
Make a 90% confidence interval estimate of today's population mean level of anxiety.
arrow_forward
Plzz explain
arrow_forward
Determine the sample size necessary to construct a 90% confidence interval with an error of 0.07 if the sample proportion is ˆpp^ = 71957195.
n =
Determine the sample size necessary to construct a 85% confidence interval with an error of 0.58 if the population standard deviation is known to be σσ = 9.29.
n =
arrow_forward
Find the value for each ta/2
Prompts
Submitted Answers
n = 18 for the 99% confidence interval for the
Choose a match
mean.
n = 10 for the 90% confidence interval for the
Choose a match
mean.
n = 15 for the 98% confidence interval for the
Choose a match
mean.
arrow_forward
Diameter measurements of 15 roller bearings made by a lathe for one week showed a mean of 1.824 inches. The long-term process standard deviation is 0.064 inches. What is the 95% confidence interval of the mean diameter of all roller bearings?
1.815 AND 1.833
OR
1.792 AND 1.856
OR
1.521 AND 2.838
please type clearly
arrow_forward
[Statistics] How do you solve this? Construct a 95% confidence interval for the proportion of vehicles affected by the law. Provide the numerical value of the lower and upper confidence limit.
Data: https://mcs.utm.utoronto.ca/~nosedal/data/cfcs.txt
CFC 2 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 1 2 2 2 2 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1 2 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1 1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 1 1 2 1 2 2 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 2 1 1 1 1 2 1 1 1 1 1 1…
arrow_forward
zy Section 7.2- MAT 240: Applied S X
O https://learn.zybooks.com/zybook/MAT-240-J4373-OL-TRAD-UG.22EWA/chapter/7/section/2?content_resource id=5..
A Q
ary > MAT 240: Applied Statistics home > 7.2: Confidence intervals for population proportions
E zyBooks catalog
Help/FAQ
387674.1891676. may?
Start
Understanding student demographics is important for a college in deciding what programs will most
benefit students. A sample of students is taken to determine what proportion of students identify as
Hispanic or Latino. The results of the sample are shown below.
Student sample
HIspanic/Latino (x)
Sample size (n)
68
400
Confidence Level
95%
Critical Value
1.96
Margin of Error
0.037
What is the population parameter?
Pick
What is the point estimate for the population proportion? p = Ex: 0.99
The data suggests a Pick v confidence exists that the proportion of students who identify as Hispanic
or Latino is between Ex: 0.123
Check
Try again
Feedback?
-arch
72°F A a O
57
PrtSc
Insert
Delete
F6
F8
F9…
arrow_forward
Lifetime of electronics: In a simple random sample of 100 electronic components produced by a certain method, the mean
20
lifetime was 125 hours. Assume that component lifetimes are normally distributed with population standard deviation o =
hours. Round the critical value to no less than three decimal places.
Part: 0 / 2
Part 1 of 2
(a) Construct an 80% confidence interval for the mean battery life. Round the answer to the nearest whole number.
An 80% confidence interval for the mean battery life is <µ <.
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning

Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning

Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON

The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Related Questions
- total plasma volume is important in determining the required plasma component in blood replacement therapy for personal growth and surgery plasma volume is influenced by the overall health and physical activity of an individual suppose that a random sample 40 mile firefighters are tested in that they have a plasma volume sample mean of x=37.5 ml/kg assume thqy o=7.70 ml/kg for the distribution of blood plasma. Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? Lower limit? Upper limit? (Round your answers to two decimal places)arrow_forwardWhat critical value of t* should be used for a 95% confidence interval for the population mean based on a random sample of 21 observations? Find the t-table here. t* = 1.721 t* = 1.725 t* = 2.080 t* = 2.086arrow_forwardCreate a confidence interval for a population proportion for a point estimate of 0.6 with a margin of error equal to $0.06. ( , ) [three decimal accuracy] [three decimal accuracy] Determine the z-scores corresponding to a 90% confidence interval. negative z-score = [three decimal accuracy] positive z-score = [three decimal accuracy]arrow_forward
- How do you solve these problems?arrow_forwardtotal plasma volume is important in determining the required plasma component in blood replacement therapy for personal growth and surgery plasma volume is influenced by the overall health and physical activity of an individual suppose that a random sample 50 male firefighters are tested in that they have a plasma volume sample mean of x=37.5 ml/kg assume thqy o=7.20 ml/kg for the distribution of blood plasma A) when finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) B) find the sample size necessary for a 99% confidence level with maximal margin of error E= 2.10 for the mean plasma volume in male firefighters round to nearest whole numberarrow_forwardCreate a 95% confidence interval for the population proportion of Orange candies. sample size is 30, point estimate is 0.44, critical z value is 0.152. Standard error is 0.602. Margin of error is 0.017 what is the lower bound and upper bound and interpretation?arrow_forward
- APA Format - Google Docs entral X e.com/courses/84804/assignments/2104292?module_item_id=5433041 ect Zoom Home Page - InSite You can retry this question below A poll of 2816 U.S. adults found that 1522 U.S. adults, or 54.048% regularly used Facebook as a news source. Find the margin of error and confidence interval for the percentage of U.S. adults who regularly use Facebook as a news source, at the 90% level of confidence. Express all answers as percentages rounded to 2 decimal places. Do not write the percent sign. Margin of Error (as a percentage): 1.65 Confidence Interval: 52.40 Margin of Error (as a percentage): 1.96 Confidence Interval: 51.85 X% to 55.70 Margin of Error (as a percentage): 2.58 Confidence Interval: 50.47 Now find the margin of error and confidence interval for the percentage of U.S. adults who regularly use Facebook as a news source, at the 95% level of confidence. X% to 56.22 Section 9.2 and 9.3 Homework E X X to 57.61 X X% Finally, find the margin of error and…arrow_forwardI need help with this one please thank you. I need you to find the P-value, and to construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.arrow_forwardHow do I find the critical value using statcrunch and manually in a calculator for this problem? Find the critical value Zα/2 that corresponds to the given confidence level. 98%arrow_forward
- Hua Nick - Final.Exam.pdf 270% 7. The standard deviation for a large population is 3. A simple random sample is taken from this population, and this sample is used to calculate a 96% confidence interval for the population mean. If this confidence interval has a margin of error of 0.283, what is the sample size? (A) 3 (В) 112 (C) 344 (D) 432 (E) 474 立arrow_forwardFind the critical value tc for the confidence level c=0.90 and sample size n=13. tc= (Round to the nearest thousandth as neearrow_forwardP(T<=t) one-tail 0.000000525 P(T<=t) two-tail 0.0000001005 1. What is the standard error for the difference between two means? 2. Compute the test statistic3. Apply the rejection rule using the critical value approach 4. Develop a99% confidence interval of the difference between the mean annual cost of attending private and public colleges.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning

Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning

Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON

The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman