Question

2. Researchers believe that spreading fires tend to do more damage to hardwood forests than do spot fires Random and independent samples were taken and the collected data on the percent of trees scarred by fire appeared in the paper "Natural Disturbance Regimes in Hemlock-Hardwood Forests of the Upper Great Lakes Region". It was used to quantify the extent of damage in the two types of fires and appears below. Use the collected data to test if indeed spreading fires cause more damage than spot fires (there is a higher percentage of trees scarred by spreading fires compared to spot fires). Assume normality and test at the 1% significance level (18 points) Spot Fires Spreading Fires Sample Mean 15.87% 10.17% Sample Standard Deviation 9.69% 7.15% Sample Size 29 28 Assumptions Но Н. Test Statistic Rejection Region Conclusion P-value If you had tested at the 5% significance level, would your conclusion have changed? Explain (3)

Answer 1

1: spreading fires, 2: spot fires. Assumptions : 1. Each population is normal. 2. Samples are random and independent. 3.population variances are unequal. Ho: Mi = 12; H:MI > H2 TI - Tp. Test statistic : ttest = – == 2.533 V + V ni 12 + /n3 =52 (appprox) Rejection region : dof = * +_ (si/ni + s/n2)2 ni-1 T 12-1 So, at 1% significance level, at dof = 52, for right -tailed tcritical = 2.40,.. Rejection region :t > 2.40

Conclusion : Since ttest falls in rejection region, we reject null hypothesis and conclude that at 1% significance level, spreading fires cause more damage than spot fires. P - value = Pr(t > 2.533) = 0.00718 If significance level was 5% still p-value < 0.05 = significance level so still previous conclusion remains the same that spreading fires cause more damage than spot fires.