Question

An environmentalist wants to determine the relationship between the number of fires in thousands, and the number of acres burned in hundreds of thousands. Based on the data, decide in the correlation is significant at alpha = 0.05.

Number of fires (x) - 73 | 74 | 58 | 48 | 80 | 65 | 54 | 49

Number of acres burned (y) - 64 | 46 | 22 | 23 | 51 | 12 | 29 | 10

Showing all work determine where to reject or not reject the null hypothesis.

HELP!!!

Answer 1

Solution:

Here, we have to use t test for the population correlation coefficient.

The null and alternative hypotheses for this test are given as below:

H0: ρ = 0

Ha: ρ ≠ 0

This is a two tailed test.

We are given

Level of significance = α = 0.05

From given data, we have

Sample size = n = 8

df = n – 2 = 8 – 2 = 6

Critical value = 2.446912

(by using t-table)

Sample correlation coefficient = r = 0.768787

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.768787*sqrt(8 - 2)/sqrt(1 - 0.768787^2)

t = 2.944678

Test statistic = 2.94

Critical value = 2.45

Test statistic > Critical Value

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a statistically significant relationship between the number of fires in thousand and the number of acres burned in hundreds of thousands.