<< Chapter < Page Chapter >> Page >

Saad, Lydia. “Three in Four U.S. Workers Plan to Work Pas Retirement Age: Slightly more say they will do this by choice rather than necessity.” Gallup® Economy, 2013. Available online at http://www.gallup.com/poll/162758/three-four-workers-plan-work-past-retirement-age.aspx (accessed July 2, 2013).

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) = ( p E B P , p   + E B P ) =   ( p z p q n , p + z p q n )

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 = 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 ~ N ( p , p q n ) 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 α 2 p q n

Confidence interval for a proportion:

( lower bound, upper bound) = ( p E B P , p + E B P ) = ( p z p q n ,   p + z p q n )

n =   z α 2 2 p q E B P 2 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 p   = x n

Questions & Answers

How do you get log of normal population
Shan Reply
what is the probability of getting no head face up in three tosses of a fair coin?
Epara Reply
In how many ways can probability be assigned to an event of interest?
Epara
Hey guys can someone help me with combinations and permutations
Lion
Phone lines on an airline system are occupied 50% of time assume that 10 calls are placed to the airline. What is the probability at least 1 call the lines are occupied?
Highness Reply
Phone lines on an airline system are occupied 50% of time assume that 10 calls are placed to the airline. What is the probability at least 1 call the lines are occupied?
Highness Reply
Why is the method of selecting the sample even more important than the size of the sample?
Nana Reply
formulaas for gruoped and ungrouped of quartiles
chatered Reply
Why is the method of selecting the sample even more important than the size of the sample?
Nana
una empresa productora que participa en el mercado de lapices tiene la siguente funcion de demanda Qd=a la raiz de 9 -9p si la elasticidad precio de demanda de la empresa es epd=0,5 determinar a) hallar el precio y cantidad
Jany Reply
find the mean mew and the standard devation sigma of the given population 9.8,10.2,10.4,9.8,10.0,10.2,9.6
Vaneza Reply
1. A card is drawn at random from an ordinary deck of 52 playing cards.* *Find the probability that it is* (a). an ace (b). a jack of hearts (c). a three of clubs or a six of diamonds (d). a heart (e). any suit except hearts (f). a ten or a spade (g). neither a four nor a club. *Hint:* 1st determine how many of the following is in a deck of cards. A deck of cards have 52 cards ♠️- Club ♣️ - Spade ♥️ - Heart ♦️- Diamond
Agness Reply
a measure of central tendency is a typical value around which other figures congregate
Anand Reply
hmm mean mode median
Umar
nothing
farri
Y = alpha0 + alpha1X1 + E what is this equation
Musawenkosi Reply
An estimated linear regression equation
Carlos
Thank you
Musawenkosi
simple linear regression .. where Alpho zero is reg constant ( intercept of the reg line) and Alpha1 is the regression coefficient ( slope of the regression line)
Umar
null and altarnate hypothesis are the statement about
farri Reply
about any population of interest
Umar
don't know
farri
I said we give hypothesis about any population and mean , in null hyp we say sample mean is equal to the population mean where as in alternate hyp we say sample mean is not equal to the pop mean .. to test these things we use students test statistics commonly
Umar
ok thnx
farri
welcome
Umar
probability of getting one black card
kaynat Reply
from a standard deck?
Umar
it will be 1/2
Umar
coz there are 26 blacks card out of 52 in a deck
Umar
so prob of getting a black card out of the deck = 26/52 = 1/5 =0.5
Umar
when are not two events mutually exclusive? 1) they overlap in a venn diagram 2) Probability of one affects the other
Junaid Reply
both
Umar
A stenographer claims that she can take dictation at the rate of 120 words per minute can we reject her claim on the basis of 100 trails in which she demonstrates a mean of 116 words with a variance of 225 words
Aromal Reply
the hypothesis to be tested is the claim to be tested
smita
H0= 120,Ha not equal to 120 x bar =116,s=225,n=100
smita

Get the best Introductory statistics course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask