Question

A researcher wanted to learn whether the urge to smoke cigarettes was associated with the number of times a person exercised in the last week. So the researcher gathered 10 who smoke for the study. Participants were asked to rate their urge to smoke on a scale of 0 (no urge) to 10 (extreme urge), and to give the number of times each had worked out in the last week. Using the data below, an alpha of .05 (two-tailed), use a Pearson correlation to determine the outcome.

n the box below, provide the following information:

Null Hypothesis in sentence form (1 point):

Alternative Hypothesis in sentence form (1 point):
Critical Value(s) (2 points):

Calculations (4 points): Note: the more detail you provide, the more partial credit that I can give you if you make a mistake.

Outcome (determination of significance or not, and what this reflects in everyday language, 2 points)

Participant	Smoking Urge	Workouts
1	6	2
2	7	1
3	3	3
4	3	5
5	5	1
6	3	2
7	5	4
8	6	0
9	4	2
10	3	3

Answer 1

x	y	(x - xbar)	(y - ybar)	(x - xbar)*(y - ybar)	(x - xbar)²	(y - ybar)²
6	2	1.5	-0.3	-0.45	2.25	0.09
7	1	2.5	-1.3	-3.25	6.25	1.69
3	3	-1.5	0.7	-1.05	2.25	0.49
3	5	-1.5	2.7	-4.05	2.25	7.29
5	1	0.5	-1.3	-0.65	0.25	1.69
3	2	-1.5	-0.3	0.45	2.25	0.09
5	4	0.5	1.7	0.85	0.25	2.89
6	0	1.5	-2.3	-3.45	2.25	5.29
4	2	-0.5	-0.3	0.15	0.25	0.09
3	3	-1.5	0.7	-1.05	2.25	0.49
xbar	ybar	Σ(x - xbar)	Σ(y - ybar)	Σ(x - xbar)*(y - ybar)	Σ(x - xbar)²	Σ(y - ybar)²
4.5	2.3	0	1.78E-15	-12.5	20.5	20.1
r = Σ(x - xbar)*(y - ybar)/√Σ(x - xbar)²*Σ(y - ybar)²	-0.616

The hypothesis being tested is:

H₀: ρ = 0

H₀: The urge to smoke cigarettes was not associated with the number of times a person exercised in the last week.

H_a: ρ ≠ 0

H_a: The urge to smoke cigarettes was associated with the number of times a person exercised in the last week.

The critical value is 0.632.

Pearson's r is -0.616.

Since 0.61 < 0.632, we cannot reject the null hypothesis.

Therefore, we cannot conclude that the urge to smoke cigarettes was associated with the number of times a person exercised in the last week.