Correlation/ Correlation Hypothesis Testing

Question 1

What does correlation mean?

Answer 1

The measure of the relationship between two variables

Question 2

What is the product moment correlation coefficient (r) ?

Answer 2

a measure of the correlation between two variables
-1 ≤ r ≤ 1

Question 3

What is the interpretation when r is ± 1?

Answer 3

Perfect linear correlation

Question 4

What is the interpretation when r is ± 0.9 ?

Answer 4

Very strong linear correlation

Question 5

What is the interpretation when r is ± 0.8?

Answer 5

Strong linear correlation

Question 6

What is the interpretation when r is ± 0.7?

Answer 6

Fairly strong linear correlation

Question 7

What is the interpretation when r is ± 0.6 ± 0.5 ± 0.4 ?

Answer 7

Moderate Linear Correlation

Question 8

What is the interpretation when r is ± 0.3 ± 0.2 ?

Answer 8

Weak Linear Correlation

Question 9

What is the interpretation when r is ± 0.1± 0 ?

Answer 9

No linear correlation

Question 10

What are the steps on the calculator to find r?

Answer 10

menu 6 (stats)
2 (y=a + bx)
Put values for x and y in
Press OPTN
4 - Regression Calc
r =

Question 11

If the r value is bigger than the critical value what do you do to the Ho?

Answer 11

r > critical value
Reject Ho
Therefore there is significant evidence to support hypothesis

Question 12

When do you reject the Ho? (correlation hypothesis testing)

Answer 12

r value > critical value
probability (p-value) < sig level / sig level > probability
significant evidence to support hypothesis

Question 12

When do you fail to reject the Ho? (correlation hypothesis testing)

Answer 12

r value < critical value
probability (p-value) > sig level
no significant evidence to support hypothesis

Question 13

What are the different methods you can use in correlation hypothesis testing?

Answer 13

Compare r value with critical value

P value method:
compare probability with sig level

Question 14

How do you work out σX̄ ?

Answer 14

σX̄ = σ/√n

Question 15

How do you work out z ?

Answer 15

z = X̄ - μ /σ/√n

Question 15

What are the different methods you can use for Hypothesis testing for means?

Answer 15

critical value method
z method
P value method

Question 16

What are the steps for the p value method? (hypothesis testing for means)

Answer 16

Work out σX̄
Find the P( X̄ > X̄) using Normal distribution
Compare the Probability you get (p-value) with the significance level
If P-value < sig level then reject Ho

Question 17

What are the steps for the Critical Value method? (hypothesis testing for means)

Answer 17

Work out σX̄
If μ > value then sig level will be on right side so it will the inverse area of 1 - sig level
If μ < value then sig level will be on left side so the inverse area will be the sig level
Find the inverse normal
Answer you get is the critical region
If X̄ lies in critical region then reject Ho

Question 18

What is the Z method? (hypothesis testing for means)

Answer 18

Work out z value (need z equation for this)
Draw Normal distribution bell
Do inverse normal, this gives you the critical z value
Compare z value with critical z value
If z value > critical z value then reject Ho

Question 19

If you reject Ho what does this mean?

Answer 19

There is significant evidence to support the hypothesis

Question 20

If you fail to reject Ho what does this mean?

Answer 20

There is not significant evidence to support the hypothesis

Question 21

When do you reject the Ho (hypothesis testing for means) ?

Answer 21

If:
z value > critical value
P value < sig level
Sample mean lies in critical region

Question 22

When do you fail to reject the Ho (hypothesis testing for means) ?

Answer 22

If:
Z value < critical value
P value > sig level
Sample mean does not lie in the critical region

Question 23

If the z value > critical value, what do you do?

Answer 23

Reject Ho

Question 24

If critical value > z value, what do you do?

Answer 24

Fail to reject Ho

Question 25

If P value < sig level, what do you do?

Answer 25

Reject Ho

Question 26

If the sig level < p value, what do you do?

Answer 26

Fail to reject Ho

Question 27

If the sample mean lies in the critical region, what do you do?

Answer 27

Reject Ho

Question 28

If the sample mean does not lie in the critical region, what do you do?

Answer 28

Fail to reject Ho

Question 29

If r > critical value, what do you do?

Answer 29

Reject Ho

Question 30

If r < critical value, what do you do?

Answer 30

Fail to reject Ho