# STA 205 Lecture 5: Packet 5 - Confidence Interval for p

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Packet 5: Confidence Interval for the Population Proportion Textbook pages: 428 – 442

After completing this material, you should be able to:

• construct a confidence interval for the proportion using the appropriate format.

• state when it is valid to use this procedure.

• explain what “confidence” means.

• calculate the sample size needed to estimate the proportion within a specified margin of error for a desired degree

of confidence.

NKU and Murray State University are two regional state schools in Kentucky. While both of these schools draw from the

surrounding states to fill its student body, most believe that the majority of students are from the state of Kentucky. The

Council of Postsecondary Education would like to sample students from both schools to estimate the proportion of

students from KY. A sample of 562 NKU students found that 373 were from KY. Similarly, a random sample of 485 Murray

State students found that 330 were from KY.

Given only this information, what would your estimate be for the proportion of all NKU students that are from KY? What

would the estimate be for all Murray State students that are from KY?

Do you have any confidence that these two estimates are exactly correct? What could be done to improve your estimate?

What is a confidence interval?

We want to develop a confidence interval which will be used to estimate the population proportion. What will the formula

for this interval be?

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NUU F35 20.6637 Weestimate 66.3T lof ALLWKU Students are from KY

MSU pot Goffs 0.6804 Weestimate 6804lof All MSU students arefrom KY

The estimates are good bcthey are based from data from random samples

But we have no confidence that they are exactly correct

Aconfidence interval ESTIMATES an unknown population parameter

based on data from asample with some prespecified degree of

certainty level of confidence

basic form point estimate margin of error

Ilaculatedfromthe wiggle room

sample Howuncertaindoyoureally feelB

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Formula pat zHttp

WIs

TR

Not calculated accounts

its acritical for variability

value based on in the

level of confidence sample

comes from the actual corresponding

probability then find Zoo to find the

value of Zlook up 0.05 in the middle

of the normal table

ff

21.645 O21.645

page 2

STA 205 Notes Buckley Fall 2018

When calculating the confidence interval, the margin of error requires a critical point from the normal distribution. Let’s

fill in the table below with critical values associated with common levels of confidence:

Level of

confidence

90% 95% 96% 98% 99%

z critical value

Step 1:

Step 2:

Step 3:

Steps in a Confidence Interval

Formula Alert!!

This formula will be given on

the formula sheet.

EVERY confidence interval we do will follow these same

three steps – start to commit them to memory!!

This table will be

given on the exam.

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1.645 1.96 2.054 2.3262.576

4Stays constant

Give Formula for interval

Formula patzpaltry

1h

Calculate confidence Interval

a

need Er

sampleinfo table at top of the page

Interpert the interval Mustinclude thelevel of

confidence limits of the interval and context