BUS304 – Chapters 6, 7, 8,12 1

Review for Exam 2 (Ch.6,7,8,12)

Ch. 6 Sampling Distribution

Despite interest in population mean (µ),

most of the time we only study a sample

sample mean (x).

Central Limit Theorem - IF

(1) the population has mean and variance 2, and

(2) the sample size n is large enough,

THEN: the sample mean x follows a normal distribution

sampling error = x

x

22x

2x x

μ =μ=500

σ 25σ = =0.5

n 50

σ = σ = 0.5 0.707

BUS304 – Chapters 6, 7, 8,12 2

Ch. 7 Estimating Population Mean

The confidence interval for population mean using sample data:

when population variance known

when population variance unknown

Determining sample size (pilot sample)

2x Z

n

2

-- (1 )*100% is the confidence level;

1--- Z is the z-score which makes P(0<z<1)= ;

2-- x is the sample mean;

-- is the standard deviation of sample mean.n

2x

n

st

2

2

2Z

Z required error n required errorn

BUS304 – Chapters 6, 7, 8,12 3

Ch. 8 Hypothesis Tests

Hypothesis Tests are set of methods

and procedure to study the reliability of

claims about population parameters The mean price of a beach house in Carlsbad is

at least $1million dollars

One tail (Upper / Lower), Two Tail

Example of Upper Tail test, population variance

known (else use t distribution)

H0: μ ≥ $1million

HA: μ < $1million

Reject when the sample mean is too high

H0: μ ≤ 3

HA: μ > 3

z Decision rule

If zx > z, reject H0

If zx ≤ z, do not reject H0

xZ = (x- ) ( / n )

BUS304 – Chapters 6, 7, 8,12 4

Ch. 12 Correlation & Regression

Examine the relationship among two or more random variables

Correlation (r) The value will be from -1 to 1,

Measures the degree of linearity

H0 : ≥ 0, HA: < 0

• If t < t, reject the hypothesis H0,

• If t ≥ t, do not reject the hypothesis H0.

Regression Model

x (independent), y (dependent) variables, R2=r2 measure of goodness of fit

Positive Relation

21

2

rt

r

n

yi = 0 + 1 * xi + i