Exam (elaborations)
MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions-PASS
- Course
- Institution
MATH 225N Week 5 Assignment: Central Limit Theorem for Proportions
[Show more]
Seller
Follow
ELITESOLUTIONS
Reviews received
Content preview
CentraLl i roportionmiTt s
heoremfoP
r
Week5Assi
gnment:
of the sam 1A dental student is conducting a study on the number of people
who visit
their dentist regularly. Of the 520 people surveyed, 312 indicated that they
had visited their dentist within the past year.
Find the population proportion, as well as the mean and standard
deviation pling distribution for samples of size n=60.
Correct answers:
10 point 6 0 0 $0.600$0.600
0 point 6 0 02
$0.600$ 0.600
0 point 0 6 33 $0.063$
0.063
The population proportion is p=312520≈0.600. This is also the mean of
the sampling distribution:
μp^=p=0.600
For samples of size n=60, the standard deviation of the sampling
distribution is
σpˆ=p(1−p)n−−−−−−−√=0.600(1−0.600)60−−−−−−−−−
−−−−−√≈0.063
2. From recent census data, it is discovered that the proportion of the adults
in the United States who are first generation Americans is 14%. For a
random sample of size 500, what is standard deviation for the sampling
distribution of the sample proportions, rounded to three decimal places?
---Given the population proportion p=14%=0.14 and a sample size of
,n=500, the standard deviation of the sampling distribution of sample
proportions is
σpˆ=p(1−p)n−−−−−−−√=0.14(1−0.14)500−−−−−−−−−−
−−√≈0.016
, 3. From recent survey data, a car buying business finds that 12.5% of the
proportion of adults in a city would be likely to use their services. For a random
sample of 115 people, what is standard deviation for the sampling distribution
of the sample proportions,
rounded to three decimal
places?
Given the population proportion p=12.5%=0.125 and a sample
size of n=115, the standard deviation of the sampling distribution
of sample proportions is
σpˆ=p(1−p)n−−−−−−−√=0.125(1−0.125)115−−−−−−−−−
−−−−−√≈0.031
4. Question
From recent survey data, its known that the proportion of adults in the United
States who are smokers is 18%. For a random sample of size 150, what is
standard deviation for the sampling distribution of the sample proportions,
rounded to three decimal places?
Given the population proportion p=18%=0.18 and a sample size of
n=150, the standard deviation of the sampling distribution of sample
proportions is σpˆ=p(1−p)n−−−−−−−√=0.18(1−0.18)150−−−
−−−−−−−
−−√≈0.031
5.A small community college has a population of 986 students, 252 of
whom them are considered non-traditional students.
Find the population proportion, as well as the mean and standard
deviation of the sampling distribution for samples of size n=40.
Round all answers to 3 decimal places.
The population proportion is p=252986≈0.256. This is also the mean of
the sampling distribution:
μp^=p=0.256
For samples of size n=40, the standard deviation of the sampling
distribution is
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ELITESOLUTIONS. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67096 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now