Question

In conducting a hypothesis test for a correlation, the correct probability distribution to use is the F distribution.

True

False

Utah State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed:

GPA	HOURS
3.14	25
2.75	30
3.68	11
3.22	18
2.45	22
2.80	40
3.00	15
2.23	29
3.14	10
2.90	0

If the university wished to test the claim that the correlation between hours worked and GPA is negative, the following null and alternative hypotheses would be appropriate:

H_o: ρ < 0.0

H_a: ρ ≥ 0.0

T/F

When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

True

False

Answer 1

Solution:

Question 1) In conducting a hypothesis test for a correlation, the correct probability distribution to use is the F distribution.

This is False , since we use t distribution to conduct a hypothesis test for a correlation.

Question 2)

If the university wished to test the claim that the correlation between hours worked and GPA is negative, the following null and alternative hypotheses would be appropriate:

H_o: ρ < 0.0

H_a: ρ ≥ 0.0

This is False.

Since null hypothesis is hypothesis of no difference and always includes equality (=) sign.

Thus it can not be strictly < or strictly >

Question 3) When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

This is False.

Since correlation coefficient lies between -1 to +1

It may be negative or positive, depending on type correlation or nature of relationship between two variables.

If direction of changes is same then there is positive correlation and if direction of changes is opposite then there is negative correlation.