Question

Is the proportion of wildfires caused by humans in the south lower than the proportion of wildfires caused by humans in the west? 372 of the 502 randomly selected wildfires looked at in the south were caused by humans while 395 of the 510 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the  = 0.10 level of significance?

1. For this study, we should use
   t-test for a population, mean t-test for the difference between two independent population, means t-test for the difference between two dependent population, means z-test for the difference between two population proportions, z-test for a population proportion
2. The null and alternative hypotheses would be:

   Select an answer p1 μ1  Select an answer > < = ≠  Select an answer p2 μ2  (please enter a decimal)   

   Select an answer p1 μ1  Select an answer ≠ > < =  Select an answer p2 μ2  (Please enter a decimal)

3. The test statistic t or z? =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? >, ≤ ,
6. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of wildfires caused by humans in the south is lower than the population proportion of wildfires caused by humans in the west.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 502 wildfires that were caused by humans in the south is lower than the proportion of the 510 wildfires that were caused by humans in the west.
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of wildfires caused by humans in the south is lower than the population proportion of wildfires caused by humans in the west.
   • The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of wildfires caused by humans in the south is equal to the population proportion of wildfires caused by humans in the west.

Answer 1

a)

z-test for the difference between two population proportions,

b)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

c)

p1cap = X1/N1 = 372/502 = 0.741
p2cap = X2/N2 = 395/510 = 0.7745
pcap = (X1 + X2)/(N1 + N2) = (372+395)/(502+510) = 0.7579

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.741-0.7745)/sqrt(0.7579*(1-0.7579)*(1/502 + 1/510))
z = -1.244

d)

P-value Approach
P-value = 0.1067

e)

As P-value >= 0.1,

f)

fail to reject null hypothesis.

g)
Thus, the final conclusion is that ...
The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of wildfires caused by humans in the south is lower than the population proportion of wildfires caused by humans in the west.