Question

Conduct a Pearson correlation coefficient test (r) using the following data:

A researcher is interested in studying the relationship between team fandom and social perception. She asks participants how much they love the Los Angeles Dodgers and then asks another participant in the same study how cool they think that person is. The data is as follows, and is on an 11-point scale:

Participant	Fandom	Perception
A	10	11
B	1	1
C	9	10
D	10	10
E	5	7
F	1	1
G	11	11

a. State the groups being tested.

b. State the Null and Research hypotheses.

c. Determine the values necessary to calculate the r statistic.

d. Calculate the r statistic.

e. Determine the critical value using a two-tailed hypothesis test at a 0.05 p level.

f. Make a decision about the hypothesis.

Answer 1

Solution:-

a) The groups being tested are participants from A to G.

b)

Null Hypothesis H_O: The population correlation coefficient is not significantly different from 0.( )

Alternate Hypothesis H_A: The population correlation coefficient is significantly different from 0.( )

Significance level = 0.05

c)

d) The correlation coefficient is given as:

r = 0.9848

Degree of freedoms:-

D.F = n - 2

D.F = 5

e)

t_Critical = + 2.571

Rejection region is - 2.571 > t > 2.571

Test statistics:-

t = 1.977

Since t value(1.977) lies in the rejection region, hence we have to reject the null hypothesis.

From this we can conclude that there is a significant linear relationship(correlation) between between team fandom and social perception.