Stat 250 Review

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Final Exam Review Part VI
Definitions and Terms: Know the major definitions and terms for example 1.
2.
3.
4.
5.

6.
7.
8.
9.
10.
11.
12.
13.
14.

Population
Sample
Descriptive Statistic
Inferential Statistics
Parameter vs Statistics
Variable
a. Categorical
Statistic
estimates Parameter
b. Quantitative
estimates
, sample mean
, population
i. Discrete
mean
s, sample standard estimates
, population
ii. Continuous
deviation
standard deviation
Random Variable
estimates P, population
ˆ
p , sample
Sampling Distributions
proportion
proportion
Parameter (Defines a population)
Statistic (calculated from sample to estimate a parameter)
Central Limit Theorem
Law of Large Numbers
Confidence Level
(1- )*100
Type I error (rejecting the null hypothesis when in fact it is true) Type II error (not rejecting the null hypothesis when in fact the null is not true) What is true

What you did

Do not
Reject H0
Reject H0

H0 true
No Error
Type I
error

Ha True
Type II
Error
No Error

15. Level of Significance (The probability of making a Type I error) 16. Interpretation of a confidence interval
17. P-value
a. The probability of making a type I error based on your sample b. The probability, computed supposing the H0 to be true, that the test statistic will take a value at least as extreme as that actually observed.

18. Interpretation of a test of significance (hypothesis test)

Types of Problems
1. Reading and interpreting graphs (make sure you read the labels so you know units and whether the graph is frequency (counts) or relative frequency (percents, ratios, probabilities).
2. Calculating Measures of Center
a. Mean
b. Median
3. Calculating Measures of Spread
a. Range
b. You will not have to calculate the standard deviation, but you must understand what the standard deviation is – the average distance each data value is from the mean.
c. Interquartile Range (Q3 – Q1)
i. 1st quartile
ii. 2nd quartile (median)
iii. 3rd quartile
4. Shape of distributions
5. Shape of distributions and effects on Mean and Median
6. Effects of outlier and skewed distribution
a. Non-resistant measures of Center and Spread: mean and standard deviation b. Resistant measures of Center and Spread: median and interquartile range 7. Boxplot and 5 number summary: Min, Q1, Q2, Q3, Max

8. Binomial Distribution
a. Calculating the mean , =np

np(1 p)

b. Calculating the standard deviation,

c. Finding probabilities using the CDF output from MINITAB
9. Calculating Probabilities for a Normal distribution (Knowing how to use Table A, the standard normal distribution)
a. Standardizing any normal random variable
i.

z

x

b. Unstandardizing any normal random variable
i. x
z
10. Sampling distributions
a. Sampling distribution of the sample mean – samples of size n i. Mean, x= (can be calculated even if we do not know the shape of the distribution)
ii. Standard deviation,

x

n

the shape of the distribution)

(can be calculated even if we do not know

iii. Shape of sampling distribution
1. If population the sample came from is normal, all sampling distributions of any size are normal
2. If the shape of the population is unknown or is NOT normal, then the sampling distribution of the sample mean is normal only if the sample size is 30 or more by the Central Limit Theorem (The shape of the sampling distribution becomes approximately Normal if the sample size is large enough. In our class a sample of size 30 or more is “large enough” to assume the sampling distribution is approximately Normally distributed.)

iv. Knowing how to compute probabilities based on the sampling distribution of the sample mean when applicable.
v. Inferential Techniques based on sampling distribution when conditions are met (SRS and Normality)
1. Estimation – Confidence Intervals : statistic margin of error (margin of error = critical value * standard error)
a.
known:
i.

X

z

/2...
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