DISCUSSION 10
April 19-20
•Statistical Inference :
Statistical inference deals with drawing conclusions about population parameters from an analysis
of the sample data.
•Point Estimator and Standard Error(SE) :
A statistic intended for estimating a parameter is called a point estimator, or simply an estimator.
The standard deviation of an estimator is called its standard error.
•Point Estimation of the Mean :
Estimator: ¯
X
S.E.( ¯
X) = σ
√n
Estimated S.E. ( ¯
X) = S
√n
For large n, the 100(1 - α)% error margin dis Zα/2σ/√n=Zα/2S.E.(¯
X).
(If σis unknown, use Sin place of σ.)
•Determing the Sample Size :
To be 100(1 - α)% sure that the error of estimation |¯
X−µ|does not exceed d, the required sample
size is
n= (Zα/2σ
d)2
Example 1. Determine the point estimate of the population mean µand its 100(1 −α)% margin
of error in each case.
a. n= 150, ¯x=86.2, s= 9.56, 1 - α= .975
b. n= 70, Pxi= 852, P(xi−¯x)2= 215, 1 - α= .95
Example 2. Fifty-eight trout caught in a lake had average weight = 4.37 pounds and standard
deviation = 1.61 pounds. Fron these data, estimate the mean weight of catchable trout in this lake
and give a 90% error margin.
Example 3. For each case, determine the sample size n that is required for estimating the popu-
lation mean. The population standard deviation σand the desired error margin are specified.
a. σ= 3.8, 95% error margin = .75
b. σ= 125, 80% error margin = 4.5
Example 4. Assume that the standard deviation of the heights of five-year-old boys is 3.5 inches.
How many five-year old boys need to be sampled if we want to be 90% sure that the population
mean heightis estimated within 5 inches?
Off. Hour: R 2:30-4:30 1 1245F MSC