# 8.3 A population proportion  (Page 5/24)

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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)

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

How do you get log of normal population
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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?
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?
Why is the method of selecting the sample even more important than the size of the sample?
formulaas for gruoped and ungrouped of quartiles
Why is the method of selecting the sample even more important than the size of the sample?
Nana
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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
a measure of central tendency is a typical value around which other figures congregate
hmm mean mode median
Umar
nothing
farri
Y = alpha0 + alpha1X1 + E what is this equation
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)
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null and altarnate hypothesis are the statement about
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
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welcome
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probability of getting one black card
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
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when are not two events mutually exclusive? 1) they overlap in a venn diagram 2) Probability of one affects the other
both
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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
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 By By OpenStax By Rohini Ajay By OpenStax By Szilárd Jankó By OpenStax By Tamsin Knox By JavaChamp Team By By Jugnu Khan By Brooke Delaney