Download Normal distribution

Applied Statistics / 2015
2015/9/30
LECTURE 3
Manifest sample to population according to the shape.
Normal distribution
Theoretical concept
Mean, median, mode same
Infinite magnitude, tail does not touch the baseline
Bell-shaped, real world, p399 figure
Standard deviation and z-score (standardized scores)
z = x-mean/s
mean=68, s =10
58=-1, 88=+2
Proportions of normal distribution
Standardized z scores: 85 z=1.7, , 58/min z=-1.8
Standardized normal curve
Mean of a distribution of z-scores will be zero and standard deviation is 1
34% between 0 and 1, z=±1 68.26%, z=±2 95.45%
Determining areas under the normal curve
Above 50, z=-1.8, 0.4641, 0.5, 0.9641=96.41%
above 80, z=1.2, 11.51%
validity: closeness with the normal distribution
Test normal assumption,
1. measures of skewness and kurtosis
2. Goodness of Fit test (N<=30, S-W test or N > 30, K-S test) (SPSS: descriptive,
explore, plot)
Inferential statistics: how groups differences
Sample data to unknown population
Confidence interval:
a range of scores with specific boundaries
Unknown population
Point estimate, mean, median, mode
Interval estimate, CI,95% CI
Confidence interval with small sample
sample mean and standard error of the mean
CI=mean±(z) sx
Applied Statistics / 2015
2015/9/30
standard error of the mean
(estimate of the population standard deviation), sx=s/√n
Figure 18.2 example
95.45 of 100 fall into mean ± 2 sx
Mean=40 s=8.8, n=42
sx= 8.8/√42=1.36,figure 18.3, 95% CI
t-distribution (n less than 30): smaller samples
flatter and wider, as n increases approach the shape of normal curve
CI=mean±(t) sx
95% CI, n=18, mean=5, sx=2, t=2.11 for df=17, 95% CI = 5.0±(2.110)(2.0)=(0.78,
9.22)
95% CI, n=31, mean=5, sx=2, t=2.042 for df=17, 95% CI = 5.0±(2.042)(2.0)=(0.916,
9.084)
Precise estimate by increasing sample
Homework:
A population mean = 68 and s = 10, identify the followings
1. identify standardized z-score for 80 beats/min?
2. determining the area above 80 beats/min?
3. Please use data from lecture2homework to calculate mean, standard error, 95%
confidence interval for romfl variable.
4. Please use data from lecture2homework to calculate mean, standard error, 95%
confidence interval for romabd variable.
5. draw the graph with SPSS and excel.