Question

The accompanying data were read from graphs that appeared in an article. The variables shown are the number of acres burned in forest fires in the western United States and timber sales.

Year	Number of Acres Burned (thousands)	Timber Sales (billions of board feet)
1945	209	2.0
1950	249	3.9
1955	250	4.3
1960	375	6.9
1965	72	9.8
1970	440	11.0
1975	179	11.2
1980	242	10.2
1985	437	10.1
1990	397	11.2
1995	171	3.7

(a) Compute the correlation coefficient. (Give the answer to three decimal places.)
r = _________

Is there a correlation between timber sales and acres burned in forest fires?

strong positive correlation

weak positive correlation    

strong negative correlation

weak negative correlation

no correlation

(b) The article concludes that "heavier logging led to large forest fires." Do you think this conclusion is justified based on the given data?

Yes

No    

Answer 1

The correlation coefficient between two variables can be found out using the following formula :-

We would find the correlation using following R code

x=c(209,249,250,375,72,440,179,242,437,397,171)
y=c(2.0,3.9,4.3,6.9,9.8,11.0,11.2,10.2,10.1,11.2,3.7)
r=cor(x,y)
r

r = 0.3274782

a. r = 0.327

There is a weak positive correlation between timber sales and acres burned in forest fire.

b.

Since the claim is "heavier logging led to larger forest fires"

Our null and alternative hypothesis should be as follows

Our test statistic is

or,

Under null hypothesis it follows a t distribution with n-2=9 degrees of freedom

The p-value is

= 0.163 [Value obtained from a t-table]

Since, p-value > 0.05

We fail to reject the null hypothesis at level of significance

Hence, the conclusion is not justified based on the given data.