Review Material

Question 0

Sample mean

Answer 0

X-bar

X-bar = €x/n

€=sum of
n=sample size of variable x

Question 1

Population mean

Answer 1

Mu (u) = €x/N

Question 2

What is the median and how do you find it?

Answer 2

Median is the middle value

1. Sort data
2. Find the middle value
3. If even numbers in observation, average the middle two terms

Question 3

What is the mode?

Answer 3

The most frequent value

Question 4

What are some facts about standard deviation?

Answer 4

Population standard deviation = sigma - no symbol for it = square root of variance

In normal distribution:
68% of data within 1 SD of mean
95% of data within 2 SD of mean
99.7% of data within 3 SD of mean

Question 5

What is square root of variance equation?

Answer 5

S= sqr[(€(x-xbar)^2)/(n-1)]

Xbar = sample mean
X = variable
n = sample size

This calculation arrives at standard deviation (s)

Question 6

Scatter diagram

Answer 6

Relationship between two variables

Question 7

Box plot

Answer 7

Graphical display based on quartiles

Question 8

Histogram

Answer 8

Frequency for each class of measured data

Question 9

Ha or H1 in one tailed alternative

Answer 9

Alternative hypothesis -
-One tailed alternative states direction

Right tail mu (u) > number

Left tail u < number

Question 10

Two tailed alternative

Answer 10

• population mean not equal to number or fraction

- a test is two tailed when no direction is specified in the alternative hypothesis

Question 11

When do you reject the null hypothesis? Ho? (H-not)

Answer 11

-absolute value of test statistic > critical value

• reject Ho if | z-value | > critical z
• reject Ho if | t-value | > critical t

• reject Ho if p-value < significance level (inequality is reversed)

Question 12

Test statistic

Answer 12

When testing for the population mean from a large sample and the population standard deviation is known. The test statistic is given by:

z= (xbar - u)/ (sigma/sqr(n))

Question 13

Type I error

Answer 13

Alpha (symbol not shown)

P(type I error) = significance level = probability that you reject the true null hypothesis

Question 14

Type II error

Answer 14

Beta = ß = P(type II error) = probability you do not reject null hypothesis, given Ho is false

Question 15

Confidence interval (CI)

Answer 15

A range of values within which the population parameter is expected to occur.

Question 16

Factors in determining a CI:

Answer 16

1. The sample size
2. The variability in the population, usually estimated by the SD
3. The desired level if confidence

Question 17

Use normal distribution (z table) if population standard deviation (sigma) is know a and either:

Answer 17

1. Normal population
2. Sample size > 30

Equation not shown here in white book

Question 18

CI : mean t- distribution

Answer 18

Use for normal distribution when standard deviation is NOT known

• if given sample standard deviation (s), use t-table assuming normal population
• if one population, n-1 degrees freedom

Question 19

CI : proportion

Answer 19

• Use if success or failure
• normal approximation to binomial ok if (n)(pi) > 5 and (n)(1-pi) > 5, where n= sample size, pi = population proportion

Equation in white book

Question 20

Wide confidence interval if:

Answer 20

1. Small sample size
2. Large standard deviation
3. High confidence interval

*if want narrow interval, need large sample size or small standard deviation or low confidence level

Question 21

What is a simple linear regression?

Answer 21

One independent variable, one dependent variable

Y=mx+b
Y - dependent variable
X- independent variable

Question 22

What is the coefficient of determination?

Answer 22

R^2 = % of total variation in y that can be explained by variation in x
-measure of how close the linear regression line fits the points on a scatter diagram
R^2=1 perfect linear relationship
R^2=0 no linear relationship

Question 23

R is?

Answer 23

Correlation coefficient

Question 24

What is an expected value?

Answer 24

E(x) = sum of x * p(x)

-is a weighted average, also a long run average

Question 25

Characteristics of binomial distribution

Answer 25

• can result in one of two outcomes
• is discrete (integer values) 0,1,2,n
• random variable (x) is the number of successes in n trials
• each trail is success or failure
• independent trails
• constant probability

Question 26

Characteristics of normal distribution..

Answer 26

Continuous, bell shaped, symmetric

• mean = median= mode
• cumulative probability under normal curve : use Z table if know pop. Mean (mu) and pop. Standard deviation
• sample mean: use Z table if know pop. Standard deviation and either normal dist. Or n>30

Question 27

Characteristics of t- distribution

Answer 27

• continuos, mound shaped, symmetric
• applications similar to normal
• more spread out than normal
• use t if normal population but pop. Standard deviation is NOT known
• degrees of freedom =df=n-1 if estimating the mean population as one

Question 28

What is P-value?

Answer 28

The probability of getting a sample statistic as extreme (or more extreme) than the sample statistic you get from your sample given that the null hypothesis is true.

Question 29

How to use the p-value…

Answer 29

Reject Ho if p-value is less than significance level

Question 30

When there is no variation—

Answer 30

There is certainty, exact prediction, standard deviation =0

Variation =0

Question 31

High variation means that…

Answer 31

Uncertainty, unpredictable, high deviation

Question 32

What is standard error of the mean?

Answer 32

Is the standard deviation of sample mean = standard deviation/square root of n

• as n increases, standard error decreases

Question 33

What is a sampling distribution?

Answer 33

-Expected value of sample mean=population mean, but an individual sample mean could be smaller or larger than the population mean
A distribution of sample means
- it’s a random variable (population mean is a constant parameter)

Question 34

Central limit theorem (CLT)

Answer 34

• if population standard deviation is known, sampling distribution of sample means is normal (n>30)
• CLT applies even if original population is skewd