Correlation Homework

Question

A researcher wants to investigate the relationship between 3 year olds watching Sesame Street and vocabulary. She asks the parents how much Sesame Street their child watches per week then ascertains how many words that child knows. The data is as follows

Participant	Hours watching Sesame Street per week	Words known
A	8	200
B	10	210
C	4	270
D	2	250
E	4	310
F	7	309
G	3	275
H	5	290
I	6	342

a. Who are the groups being tested?

b. What are the null and research hypotheses?

c. What is the mean of X?

What is the mean of Y?

Find the deviances for both groups. (X – My) and (Y – My)

Multiply the deviances like in the lecture

Sum these.

What number do you get? ___________________________

This is the numerator

Square the deviances in X and Y

What is the Sum of Squares of X?

What is the Sum of Squares of Y?

What do you get when you multiply SSx and SSy? _______________________________

Take the square root of that ____________________________

This is your denominator

d. What is r? ______________________

e. What is the critical value? ___________________________________

f. What is your decision? ______________________________

Answer 1

a. According to the problem, there are no groups ( such as group A or group B). Thus, this is a within-group design.

b. This depends on whether it's a one-tailed hypothesis or a two-tailed hypothesis.

b.I) * So, for a one-tailed hypothesis (meaning there is a direction), we can say: we predict a positive significant relationship between the number of hours the child watches Sesame Street and the number of words the child knows.

1. For a one-tailed, null hypothesis, we can say: there will not be a positive significant relationship between the number of hours and the child watches Sesame Street and the number of words the child knows.

On the other hand:

1. For a two-tailed hypothesis( meaning there's no direction), we can say: we predict a significant relationship between the number of hours the child watches Sesame Street, and the number of words a child knows
2. For a two-tailed null hypothesis, we can say: we predict that there will not be a significant relationship between the number of hours the child watches Sesame Street and the number of words a child knows.

C.

I). X - or x axis is your independent variable( what you are manipulating - in this case, the number of hours the child watches Sesame Street) has an average of M 5.44

I.a)Y or y axis is your dependent variable ( in this case is the number of words the child knows), has an average of M= 272.89

C.II) The numerator is -361.5556 ( or - 361.56)

C.III) Sum of Squares of X (SSx): 52.22

C.IV) Sum of Squares of Y( SSy): 17,554.89

C.V) SSx X SSy: 916,755.37

C. VI) The Square root: 957.47

D) r = - 0.38

E) if it is a one-tailed: 0.58; if it is a two-tailed: 0.67.

F) There was no significant relationship between the number of hours the child watches Sesame Street and the number of words a child knows.