Question

1)A researcher believes that there is a correlation between the number of cigarettes smoked per day and intelligence.  The following data were collected on 15 smokers.  Find Pearson's r.

Number of cigarettes (X) IQ score (Y)

7    10

49 6

41    15

38   5

37 12

19    4

35 19

40   11

1 3

10 3

18 22

21 17

15 12

7    9

38    13

n=15

Sum of X= 376          Sum of Y=161  

Sum of XY= 4,317

2) Interpret the findings from Question 2 in 1-2 sentences.

3)Give two examples, each time of two variables for which the Pearson's r might be expected to be between -.7 and -1.0.

Answer 1

Answer:

1. r = 0.22271

2. The Pearson's r = 0.22271. Hence it is very less there is weak relationship in this 2 variables. As value of r is greater than 0 (>0 ) the relation is weak postive.

3. Example for which Pearson's r might be expected to be between -.7 and -1.0 are

eg 1.  As the temperature decreases, more heaters are purchased.

eg2. If a train increases speed, the length of time to get to the final point decreases.

Explanation:

Given information is

n=15

Sum of X= 376          Sum of Y=161  

Sum of XY= 4,317

1) The formula for Pearson's r

The table for calculation is

no	X	Y	X^2	Y^2	X*Y
1	7	10	49	100	70
2	49	6	2401	36	294
3	41	15	1681	225	615
4	38	5	1444	25	190
5	37	12	1369	144	444
6	19	4	361	16	76
7	35	19	1225	361	665
8	40	11	1600	121	440
9	1	3	1	9	3
10	10	3	100	9	30
11	18	22	324	484	396
12	21	17	441	289	357
13	15	12	225	144	180
14	7	9	49	81	63
15	38	13	1444	169	494
Total	376	161	12714	2213	4317

2) The Pearson's r = 0.22271. Hence it is very less there is weak relationship in this 2 variables. As value of r is greater than 0 (>0 ) the relation is weak postive.

3) The examples for which Pearson's r might be expected to be between -.7 and -1.0.

eg 1.  As the temperature decreases, more heaters are purchased. ( here "temperature" and "heaters purchased" are negatively correlated)

eg2. If a train increases speed, the length of time to get to the final point decreases. ( here "train speed" and "length of time to get to the final point" are negatively correlated)