Download Test1

STP420 Spring 2014
Review notes for Test #1 (chapters 1,3,4 and 5)
1. Know new vocabulary and symbolic notation,
for example:
• frequency, relative frequency, mean, median, mode, range, interquartlie range
quartiles, percentiles, deciles,
• types of variables in the data (quantitative (continuous or discrete), qualitative,
(categorical) )
• stem- and leaf plot, box plot,
• random variable (discrete, continuous), density curve, probability distribution of
random variable, normal and standard normal distribution curves , standardized
version of normal variable, z-score
• Law of Large numbers
• Sampling errors
• Sampling distribution of sample mean, counts, proportions
• Binomial distribution, normal approximation to binomial
• Central Limit Theorem
• symbols for population mean, standard deviation and sample mean and standard
deviation.
2. Know how to graphically represent your data and how to read and interpret
given graphs and tables.
 Box plot
 Histogram
 Frequency and Relative Frequency Table
 Stemplot
 Bar chart, Pie chrt
3. Know all measures of center and dispersion for the sample. You need to know how to
compute sample standard deviation by hand from the definition.
Make sure to know how to interpret each measure, what each tells you about the
data. Be able to compare mean and median for symmetric and skewed data. Know how
to use IQR to check for outliers in the data. Know how linear change in measurements
affects measures of center and dispersion.
4. Know how to describe the shape of the distribution (Symmetric, left skewed,
slightly right skewed etc.) from all types of data displays. Be able to decide whether
the means and standard deviations of two given distribution curves are different or
not (from the graph). Be able to point out approximate location of median and mean
of the given distribution curve (from the graphical display)
5. Know what is the density curve. Study normal and standard normal curve. Know
68-95-99.7 rule. Know the properties of normal ,standard normal curves (Center at ,
symmetry, area under=1)
Know how to find areas under standard normal and normal curves using tables, use
symmetry. Know what is z- score and what you use it for. If variable is normally
distributed, know for example what is the % that exceeds a certain value or what is the
value that marks lower 5 % of your data.
6. Know what is the random variable, discrete and continuous.
Know how to obtain the probability distribution for a random variable and how
to compute different probabilities associated with the discrete and continuous
random variables.
Know the rules for means of random variables
Be able to compute the mean o discrete random variable.
7.
Know the difference between an observational study and a designed
experiment. What are principals of experimental design? For a given study
identify experimental units, treatment, response.
Know basic experimental designs: completely randomized design, block design,
matched pairs design.
Know how to select a simple random sample (SRS) from a population by using
random numbers tables and how to make random assignments to treatments using
that table.
Know about different types of sampling procedures, know example of each:
SRS, Stratified sample, Multistage sample, Systematic random sample.
What is Voluntary response sample and what is the problem with such a sample?
8. Be aware that what is a statistics, what is a parameter. Know that variability of a
statistics decreases with increasing sample size. Spread of the sampling distribution is
about the same for fixed n, regardless of the population size, as long as population is
much larger than the sample. Know what is a sampling distribution of a statistics.
What makes a statistics an unbiased estimate of a parameter of the population?
9. Probability
Know simple probability rules:
0  P(A)  1
P(Ac)=1-P(A)
P(AorB)= P(A)+P(B)-P(AandB) for any events
P(AorB)= P(A)+P(B) for disjoint events
P(AandB)=P(A)*P(B) for independent events only
Know what is the sample space, event, what are events: Ac, AorB, AandB
List sample spaces for simple experiments, like:
Roll die once, Roll die 2 times, Select a card from an ordinary deck,
Toss two coins, Toss 3 coins
Know when events are mutually exclusive (disjoint) or independent.
How to illustrate events using Venn diagrams.
Compute probabilities from 1- way and 2-way frequency/ relative frequency tables.
Compute probability based on independence.
10. Know the sampling distribution of sample counts and sample proportion. How and
when to use a normal approximation to binomial distribution.
Binomial distribution for counts, use a calculator or binomial formula.
Know what is the sampling distribution of the sample mean ( ̄
x ), know mean and
σ
standard deviation of ( μ X̄ =μ

σ X̄ =
√n
Know how the shape of the distribution of ̄
x changes with increasing sample size n.
Know when has normal distribution, when approximately normal distribution. Know
Central Limit Theorem.
What is the standard version of ̄
x .
Use the standard version of to answer questions like:
What is P( ̄
x > 14), where is a sample mean of a sample of size 6 from normally
distributed population with mean of 10 and std. deviation of 5.