# 8.3 A population proportion  (Page 5/24)

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The Field Poll. Available online at http://field.com/fieldpollonline/subscribers/ (accessed July 2, 2013).

Zogby. “New SUNYIT/Zogby Analytics Poll: Few Americans Worry about Emergency Situations Occurring in Their Community; Only one in three have an Emergency Plan; 70% Support Infrastructure ‘Investment’ for National Security.” Zogby Analytics, 2013. Available online at http://www.zogbyanalytics.com/news/299-americans-neither-worried-nor-prepared-in-case-of-a-disaster-sunyit-zogby-analytics-poll (accessed July 2, 2013).

“52% Say Big-Time College Athletics Corrupt Education Process.” Rasmussen Reports, 2013. Available online at http://www.rasmussenreports.com/public_content/lifestyle/sports/may_2013/52_say_big_time_college_athletics_corrupt_education_process (accessed July 2, 2013).

## Chapter review

Some statistical measures, like many survey questions, measure qualitative rather than quantitative data. In this case, the population parameter being estimated is a proportion. It is possible to create a confidence interval for the true population proportion following procedures similar to those used in creating confidence intervals for population means. The formulas are slightly different, but they follow the same reasoning.

Let p′ represent the sample proportion, x/n , where x represents the number of successes and n represents the sample size. Let q′ = 1 – p′ . Then the confidence interval for a population proportion is given by the following formula:

(lower bound, upper bound)

The “plus four” method for calculating confidence intervals is an attempt to balance the error introduced by using estimates of the population proportion when calculating the standard deviation of the sampling distribution. Simply imagine four additional trials in the study; two are successes and two are failures. Calculate ${p}^{\prime }=\frac{x+2}{n+4}$ , and proceed to find the confidence interval. When sample sizes are small, this method has been demonstrated to provide more accurate confidence intervals than the standard formula used for larger samples.

## Formula review

p′ = x / n where x represents the number of successes and n represents the sample size. The variable p ′ is the sample proportion and serves as the point estimate for the true population proportion.

q ′ = 1 – p

${p}^{\prime }~N\left(p,\sqrt{\frac{pq}{n}}\right)$ The variable p′ has a binomial distribution that can be approximated with the normal distribution shown here.

EBP = the error bound for a proportion = ${z}_{\frac{\alpha }{2}}\sqrt{\frac{{p}^{\prime }{q}^{\prime }}{n}}$

Confidence interval for a proportion:

provides the number of participants needed to estimate the population proportion with confidence 1 - α and margin of error EBP .

Use the normal distribution for a single population proportion

What Is The Confidence Interval
sample mean 25, sample standard deviation 20, sample size 200, calculate the confidence interval using the given values and the original confidence level of 90%.
Can you help me in mathematical statistics problems?
yes
Kc
Pls who can help me to teach me statistics
nasir
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Rana
ok
Ekene
the power of the test is
please can anyone help me solve these questions below? I need help please.
MMSI
a)An investor wants to eliminate seven of the investments in her portfolio by selling 4 stocks and 3 bonds. In how many can these be sold if among 25 securities in the portfolio,13 are stocks and the rest bonds?
MMSI
a)If a random variable has the standard normal distribution,what are the probabilities that it will take on a value: i)Less than 1.64 ii)Greater than-0.47
MMSI
b)A random variable has a normal distribution with a mean of 60 and standard deviation 5.2.What are the probabilities that the random variable will take on a value: i)Less than 65.2 ii)Between 48 and 72?
MMSI
b)If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001,use the Poisson law to calculate the probability that out of 2000 individuals i)Exactly 3 individuals will suffer a bad reaction. ii)More than 2 individuals will suffer a bad reaction.
MMSI
b)The breakfast menu serve data popular 5-star Hotel in Accra consists of the following items: Juice-Mango,Grape,Apple. Toast-Whitewheat,Whole wheat. Egg:Fried,Hard-boiled,Scrambled. Beverage:Coffee,Tea,Cocoa.
MMSI
Continuation of the last question.Assist the Hotel manager to determine the number of possible breakfast combinations that can be served, one from each category
MMSI
MMSI
3x2x3
Vince
Are you answering the last question?
MMSI
MMSI
bias came in sampling due to
sampling error
Vikram
what is the difference between population and sample
Inam
Sample is the group of individual who participate in your study. Sample is a subset of population. Population is the broader group of people to whom you intend to generalize the results of your study.
Ekene
how do you find z if you only know the area of .0808
construct a frequency distribution
Sana
How to take a random sample of 30 observations
you can use the random function to generate 30 numbers or observation
smita
How we can calculate chi-square if observed x٫y٫z/frequency 40,30,20 Total/90
calculate chi-square if observed x,y,z frequency 40,30,20total 90
Insha
find t value,if boysN1, ،32,M1,87.43 S1square,39.40.GirlsN2,34,M2,82.58S2square,40.80 Determine whether the results are significant or insignificant
Insha
The heights of a random sample of 100 entering HRM Freshman of a certain college is 157 cm with a standard deviation of 8cm. test the data against the claim that the overall height of all entering HRM students is 160 cm. previous studies showed that
complete the question.. as data given N = 100,mean= 157 cm, std dev = 8 cm..
smita
Z=x-mu/ std dev
smita
the power of the test is
Ejaz
find the mean of 25,26,23,25,45,45,58,58,50,25
add all n divide by 10 i.e 38
smita
38
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amit
1 . The “average increase” for all NASDAQ stocks is the:
STATISTICS IN PRACTICE: This is a group assignment that seeks to reveal students understanding of statistics in general and it’s practical usefulness. The following are the guidelines; 1.      Each group has to identify a natural process or activity and gather data about/from the process. 2.
The diameter of an electric cable,say, X is assumed to be continoues random variable with p.d.f f(x)=6x(1-x); ≤x≤1 a)check that f(X) is p.d.f b) determine a number b such that p(Xb)
A manufacturer estimate 3% of his output is defective. Find the probability that in a sample of 10 items (a) less than two will be defective (b) more than two will be defective.
A manufacturer estimates that 3% of his output of a small item is defective. Find the probabilities that in a sample of 10 items (a) less than two and (b) more than two items will be defective.
ISAIAH
use binomial distribution with parameter n=10, p= 0.03, q=0.97
the standard deviation of a symmetrical distribution is 7.8 . what must be the value of forth moment about the mean in order that distribution be a) leptokurtic b) mesokurtic c) platy kyrtic intrept the obtain value of a b and c By By By Brooke Delaney By Richley Crapo By Nicole Duquette By Mary Matera By Jonathan Long By OpenStax By Sandy Yamane By OpenStax By Kevin Moquin By OpenStax