Question

A park ranger thanks that there is a relationship between the number of bugs in a forest and the total number of forest fires that aria of the forest experiences. The ranger takes a count of the number of bugs they catch in several traps over the course of the season and the number of fires that they experienced in those areas.

Number of Bugs caught (Rounded to the nearest thousand)	Number of fires that season
1	10
2	9
0	3
1	1
0	1
3	3
3	2
1	2

1. Please define what a correlation coefficient represents? (2)
2. What is the correlation coefficient for the data above? Show work for full credit? (3)
3. Does correlation imply causation? Why or why not?(2)
4. You want to test if there is correlation between the two data sets. You are going to use a .10 alpha for your study.
   1. Write down the null-hypotheses and alternative hypotheses for the test above: (2)
   2. What does the test say about the data above, is there evidence of correlation? Can we reject the null hypotheses? (2)

Answer 1

SOLUTION-

1.) A CORRELATION COEFFICIENT REPRESENTS THE DEGREE AND DIRECTION OF LINEAR RELATIONSHIP BETWEEN TWO VARIABLE. IT RANGES FROM -1 TO +1.

2.) WE USE MINITAB-16 FOR CALCULATIONS:

STEPS- ENTER THE DATA> STAT> BASIC STATISTICS> CORRELATION> SELECT THE VARIABLES> OK

OBSERVATION- THE CORRELATION COEFFICIENT IS r=0.114

3.) CORRELATION DOES IMPLY CAUSATION.

THERE SEEMS TO BE WEAK CORRELATION BETWEEN THE TWO VARIABLES HENCE THE CONCLUSION.

4.) WE WANT TO TEST IF THERE IS A CORRELATION BETWEEN THE TWO VARIABLES. THE HYPOTHESIS IS, ; IS THE POPULATION CORRELATION COEFFICIENT.

5.) SAMPLE SIZE(n) = 8

THE TEST STATISTIC IS,

HENCE,

THE P-VALUE AT 0.10 LEVEL OF SIGNIFICANCE IS 0.7881.

AS P-VALUE> 0.10, WE CANNOT REJECT THE NULL HYPOTHESIS. AND HENCE THERE IS NO SIGNIFICANT CORRELATION AMONG THE VARIABLES.

****IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.