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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: r > 0 m 1 - m 2 < 0 3. Set a straw man, i.e., null hypothesis

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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: r > 0 m1 - m2 < 0

3. Set a straw man, i.e., null hypothesis

Null hypothesis: r = 0 m1 - m2 = 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 between two variables.

Imagined and theoretical


μ between two variables.=72

μ=72

PopulationSampling Distribution


Sample size N = 36 between two variables.

μ=72

μ=72

μ=72


Sample Size N = 16 between two variables.

μ=72

μ=72


Sample Size N = 36 between two variables.

μ=72

μ=72


Central limit theorem
Central Limit Theorem between two variables.

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: between two variables.

Hypothesis: Chinese children today are overweight.

Choose a statistic: Mean weight

Past records: m = 50 lb; s = 30 lb

H1: m > 50 lb

H0: m = 50 lb

a<.01

n = 225 children ages 7 to 9;


Reject Null between two variables.

μ=50

2.32


Point estimate: between two variables.

Interval estimates:

CI90

1.64

-1.64


An example: between two variables.

Hypothesis: Children’s weight differs from past.

Choose a statistic: Mean weight

Past records: m = 50 lb; s = 30 lb

H1: m 50 lb

H0: m = 50 lb

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

n = 225 children ages 7 to 9;


-2.58 between two variables.

μ=50

2.58


Null Hypothesis between two variables.

Actually True

Actually False

NOT reject

Decision

Reject


H between two variables.0: μ = 50

Reject Null

.05

z = 1.96

μ= 50

H1: μ > 50

power

β


H between two variables.0: μ = 50

Reject Null

.01

z = 1.96

μ= 50

H1: μ > 50

power

β


Large N between two variables.

H0: μ = 50

Reject Null

.05

μ= 50

z = 1.96

H1: μ > 50

power

β


Small N between two variables.

H0: μ = 50

Reject Null

.05

μ= 50

z = 1.96

H1: μ > 50

power

β


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