Transcript Chapter 6 Statistics

Chapter 6 Statistics
Confidence Intervals
6.1 Confidence Intervals for the
Mean (Large Samples)
I.
Estimating Population Parameters
Point Estimate:
a single value estimate for a population
parameter. The most unbiased point
estimate of the population mean is the
sample mean.
Example 1 & TIY#1 (p280)
Often the point estimate is not
exact but close, so find an interval.
• Interval Estimate:
a range of values used to estimate a
population parameter
– To form an interval estimate, use the point
estimate as the center of the interval, then
add and subtract the margin of error.
– But first you need to decide how confident you
want to be that the population mean will fall
within the interval.
• Level of Confidence (c):
the probability that the interval estimate
contains the population parameter
– We usually use:
• 90%
• 95%
• 99%
z = 1.645
z = 1.96
z = 2.575
These z-scores are called the critical values (zc)
• Sampling Error: the difference between
the point estimate and the actual
parameter value
• Margin of Error (E): given the confidence
level, E is the greatest possible distance
between the point estimate and the
parameter value.
E = zc • σ
√n
When n≥30, the s can be used in place of σ.
Example 2 & TIY#2 (p282)
• CW: p287 #1-9, 15, 31
• HW: p287-288 #10-18even, 19-22, 32