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Chapter 7.3 & 7.4

# MATH 10041 Chapter 7.3 & 7.4: MATH 10041-002 ch 7.3 CLT for sample proportions & 7.4 estimating the population proportion with confidence intervals

by OC2524154

School

Kent State UniversityDepartment

MathematicsCourse Code

MATH 10041Professor

Rajeev RajaramChapter

7.3 & 7.4This

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Wednesday

10/24/18

Chapter 7 cont

7.3 Central Limit Theorem for Sample Proportions

● Central limit theorem (CLT)- used to estimate proportions on a population

○ Without needing to use simulations

○ Enables us to measure the quality of our estimation efforts

○ Has several versions

○ Some basic conditions must be met

■ Random and independent

■ Large sample size

● AND p0n⋀ ≥ 1 (1 ) 0n−p⋀≥ 1

■ Big population (N)

● 0nN ≥ 1

Recall the empirical rule (ch. 3.2)

***

Standard deviations = standard errors

If the conditions of a survey sample satisfy those required by the CLT, then the probability that

a sample proportion will fall within 2 standard errors of the population value is 95%

To find a probability…

1. Find SE =

√p (1 ) / n−p

2. Find Z-score = SE/p⋀−p

3. 2ndVARS- normalcdf:-(lower, upper, mean, SE)

a. ( ),p,mean,SE− 1 ⋀

b. ( ),1,mean,SEp⋀

i. SE = pσ⋀

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