1. State your research hypothesis in the form of a relation between two variables.

2. Find a statistic to summarize your sample data and convert the above into statistical hypothesis:

Statistical hypothesis: > 0 1 - 2 < 0

3. Set a straw man, i.e., null hypothesisNull hypothesis: = 0 1 - 2 =

0.

4. Set the alpha level and conduct the statistical test with the assumption that the null is true.

5. Make a decision with potential errors.

Sampling Distribution of a Statistic

Imagined and theoretical

μ=72μ=72

nX

Population Sampling Distribution

μ=72μ=72 μ=72

nX

Sample size N = 36

μ=72

nX

Sample Size N = 16

μ=72

μ=72μ=72

nX

Sample Size N = 36

Central Limit TheoremCentral Limit Theorem

The mean of the sampling distribution of means (any statistic) equals the population mean (any parameter).

The standard deviation of the sampling distribution of means (any statistic) equals the population standard deviation divided by the square root of sample size. This is called the standard error of means.

The sampling distribution of means is normal independent of the pattern of the population distribution, given a large enough sample size (e.g., n = 30)

An example:

Hypothesis: Chinese children today are overweight.

Choose a statistic: Mean weight

Past records: = 50 lb; = 30 lb

H1: > 50 lb

H0: = 50 lb

<.01

n = 225 children ages 7 to 9; 55X

μ=50

2X

2.32 5.2Xz

55X

2225

30

nX

5.22

5055

XX

Xz

Reject Null

Point estimate:

55X1.64-1.64

28.58,72.51

264.155

64.1

XX CI90

55X

Interval estimates:

An example:

Hypothesis: Children’s weight differs from past.

Choose a statistic: Mean weight

Past records: = 50 lb; = 30 lb

H1: 50 lb

H0: = 50 lb

<.01; two tails, <.01/2 or <.005 at each tail

n = 225 children ages 7 to 9; 55X

μ=50

2X

-2.58 2.585.2Xz

55X

: Type II error

: Type I error Power

Actually True Actually False

NOT reject

Reject Decision

Null Hypothesis

μ= 50 z = 1.96

H0: μ = 50

H1: μ > 50

.05 Reject Null

β

power

μ= 50 z = 1.96

H0: μ = 50

H1: μ > 50

Reject Null

β

power

.01

power

β

μ= 50

H0: μ = 50

H1: μ > 50

.05

Reject Null

z = 1.96

Large NLarge N

Small NSmall N

power

β

.05

H0: μ = 50

H1: μ > 50

Reject Null

μ= 50 z = 1.96