Bsns102 - Hypothesis Testing For The Mean

Front 1

Hypothesis

Back 1

A claim about a population parameter

Front 2

The Null Hypothesis

Back 2

(Ho)
- the status quo
- begin with the assumption that the null hypothesis is true and try to disprove it

Front 3

When do you reject the null hypothesis?

Back 3

If there is sufficient evidence against the status quo

Front 4

The Alternative Hypothesis

Back 4

(Ha)
- the opposite of the null hypothesis
- challenges the status quo

Front 5

Notation used for null hypothesis

Back 5

Always "="

Front 6

Notation used for alternative hypothesis

Back 6

≠ or < or >

Front 7

A hypothesis test

Back 7

- based on a sample
- the sample provides evidence to either support of reject Ho

Front 8

If population is distributed normally....

Back 8

the sample mean is distributed normally

Front 9

For large samples from any distribution...

Back 9

the sample mean is distributed approximately normal by the Central Limit Theorem

Front 10

If it is unlikely to get a sample mean of _____ if in fact the population mean were ______, then?

Back 10

reject the null hypothesis

Front 11

What do you do before you start the test?

Back 11

Choose the level of significance (0.01, 0.05 or 0.10)

Front 12

What does the level of significance do?

Back 12

Defines the unlikely values of sample statistic if null hypothesis is true
- Rejection regions

Front 13

What are the result possibilities, in terms of a jury trial?

Back 13

Correct - not guilty, innocent
- guilty, guilty

Error - not guilty, guilty
- guilty, innocent

Front 14

What are the result possibilities, in terms of a hypothesis test?

Back 14

Ho True, Do not reject Ho = 1 - α
Ho True, Reject Ho = Type 1 Error (α)
Ho False, Do not reject Ho = Type II Error (β)
Ho False, Reject Ho = Power (1-β)

Front 15

If α is small...

Back 15

then burden of proof/error is high

Front 16

If α is high....

Back 16

then β is low

Front 17

Type 1 Error

Back 17

(α): rejecting null when it is actually true

Front 18

Type II Error

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(β): not rejecting null when it is actually false

Front 19

What are the 7 steps in the Hypothesis Test?

Back 19

1. State Ho Parameter; represents the status quo and contains "="
2. State Ha parameter; challenges the status quo and contains "≠" or "<" or ">"
3. Choose α (level of significance)
- determines rejection regions
- consider risk of Type I and II errors
4. Choose sample size (n)
5. Select correct test statistic
6. Collect data and calculate sample stats and test stat
Test statistic = (Sample Statistic - Null Ho Value)/Standard Error
7. Make the decision

Front 20

What does the test statistic calculate?

Back 20

How many standard errors what you have observed is away from that stated in the null

Front 21

Test Statistic

Back 21

(Sample Statistic - Null Ho Value)/Standard Error

Front 22

What is the most common method to make the decision?

Back 22

The P Value Approach - sig in SPSS

Front 23

P Value

Back 23

The probability of obtaining a test statistic at least as extreme (≥ or ≤ or both) than the observed sample value, given Ho is true
- How likely is what you have observed if the null were true

Front 24

Rule for P Value Approach

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If P is less than α, reject Ho
If p is ≥ α , DO NOT reject Ho

--> If the p value is low, reject Ho

Front 25

When do you use a Z test?

Back 25

When σ is known

Front 26

When do you use a t test?

Back 26

When σ is unknown

Front 27

What must we remember with the t test?

Back 27

Degrees of freedom (n-1)

Front 28

What do we use in a t test instead of σ?

Back 28

s