# Stat 250 Review

**Topics:**Normal distribution, Standard deviation, Sample size

**Pages:**10 (1113 words)

**Published:**November 9, 2012

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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