Download Ch. 7 Estimating population parameters and finding minimum

Ch. 7 Estimating population parameters and finding minimum sample size needed to estimate …
Recall from ch. 6 with sampling distributions that the sample proportions , means and variances are
good, unbiased estimators of the population proportions , means and variances. Note the distribution
of sample proportions and sample means is normally distributed but the distribution for variances is
skewed to the right (most data on left with very little data on the right). See page 281 in textbook.
Section 2: Estimating population proportions (percentages)
POINT vs. INTERVAL estimates (page 329)
Correct INTERPRETATION of confidence intervals (pages 330-1)
Confidence level (middle part of curve), level of significance (α – the left over and put half in each tail)
and critical values (see pages 330-2)
Margin of Error definition and formula (page 332-3)
Symbols, formulas and requirements for confidence interval estimates (CIE) for population proportions
(page 333)
Round off rule for confidence interval estimates (CIE) of population proportions (page 334)
Determining sample size required to estimate a population proportion (page 336-7)
Round off rule for sample size (page 336)
see video for examples p. 341 #22 and p. 343 #42
Section 3: Estimating population means - population standard deviation known – rare and unrealistic
POINT vs. INTERVAL estimates (page 345)
Symbols, formulas and requirements for confidence interval estimates (CIE) for population means (page
333)
Round off rules for confidence interval estimates (CIE) of population means (page 347)
Correct INTERPRETATION of confidence intervals (pages 347)
Determining sample size required to estimate a population mean (page 349-350)
NOTE: Remember we must have an normal distribution with original data OR a sample size that is large
enough (n >30) in order to use the CLT.
see video for examples p. 353 #26 and p. 354 #34
Section 4: Estimating population means - with population standard deviation unknown
More common and realistic than last section – why would we know the population standard deviation
and not have the population mean? We probably wouldn’t. If you know the population standard
deviation, then you probably know the population mean as well and wouldn’t need to estimate it.
We make a minor adjustment and use a Student t distribution instead of a normal distribution.
Degrees of freedom and finding t critical values from Table A-3 in your book (page 356-7)
Symbols, formulas and requirements for confidence interval estimates (CIE) for population means (page
357)
Important properties of a Student t distribution (page 359)
Choosing the appropriate distribution (pages 360-1)
See video for examples p.367 #22 and p. 365 #6,8,10,12
Section 5: Estimating population standard deviations and variances
Chi-square distribution (page 370-1) and Table A-4 for Chi-square critical values
POINT vs. INTERVAL estimates of variance and standard deviation (page 373)
Symbols, formulas and requirements for confidence interval estimates (CIE) for population variances
and population standard deviations(pages 373-4)
Round off rules for confidence interval estimates (CIE) of population variances and population standard
deviations - same as for estimating population means (page 374 – see step 5 of procedure)
Determining sample size required to estimate a population variances and population standard
deviations (page 376-7)
See video for example p. 370 #20
What population parameter are
estimating with a confidence interval?
Population
proportion/rate/percentage
Find the sample proportion (𝑝̂ ) which
is the point estimate.
Add and subtract margin of error to
create interval.
p̂ ± E where E =
z
2
pˆ qˆ
n
Population mean
Assumption: Original population
must be normally distributed OR
sample size is large enough (n >
30) in order to use either the t or
z distribution.
Formula: x ± E
where E =
z 
2
n
or E =
t s
2
n
Population standard deviation or
variance Find the sample standard
deviation or variance.

 (n  1) s 2 (n  1) s 2
,

2
2
 

R
L



2
 for σ

