BA 253: Business Statistics 10/08/08
Today
Confidence
Intervals
(Chapter 8)
Fri
More CI (Ch 8)
Start ICE 6
Mon (10/13)
No class!
Finish ICE 6
Weds(10/15)
No class!
Project
Proposal
Collect HW 4.
Chapter 8
Previously, we assumed μ and σ were known, then found that the sample mean
x
was approximately normal for n ≥ 30.
Reality Check: Why estimate μ if we already know it???
What if we do not know μ, but want a good estimate for it?
Ex: Survey 50 people about how much they spend on gas per week.
x
= $37, s = $19.
Is μ ≈
x
= $37? How close is the population mean to the sample mean?
With 95% certainty, what is the population mean?
oPoint Estimate: μ =
x
= $37.
oConfidence Interval: μ is in
x
± E = …………
oThere is a 95% chance that the population mean is in 37 ± 5 = ($32, $42).
Require more certainty? Interval gets bigger.
Got more data? Interval gets smaller.
What if we want the error to only be ± $1? How many samples n do we need?
oE = ………. n = ………. = 1381.
Ex: n = 100,
x
= $1200, s = $425.
What is the 98% confidence interval for μ?
How many samples are required to know μ within ± $50?
Ex: Same survey as before. With higher gas prices, have you considered switching to a
more fuel efficient vehicle?
p
= 37/50 = 74% = 0.74
Is p =
p
= 74%?
With 95% certainty, what is p?
Point Estimate: p = 74%.
Confidence Interval:
p
± E = …… = 74% ± 12% = (61%, 85%)
How many data necessary to know p within ± 5%?
E = ……, solve for n, = 303
What if we didn’t know
p
? Then assume p = ½.
At 95% confidence, how many samples n necessary to know a proportion within
± 5%? ± 1%?
Quick estimate
Fill in……….. Average Proportion
Point Estimate
Confidence Interval
