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

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19 Dec 2018
School
Department
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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
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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
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