1.)

The fire management agency wants to assess the most common cause of wildfire ignition to determine future fire management practices. Data from the past year's fire season indicate that out of 7894 fires, the two most common causes of fire were ignition due to electrical power/ equipment use (2564 fires) and debris burning during heat waves (2356 fires).

At the 95% confidence level, do the data indicate that greater proportion of fires are caused by electrical power/equipment use or by debris burning? In this problem use a test statistic as part of the analysis leading to your result (not a confidence interval). (Data attached below.)

Please type up, show, and explain all work with equations. Thank you.

Total fires

7948

Fires caused by electrical power/equipment use

2564

Fires caused by debris burning

2356

2.)

The fire management agency is assessing the impact of the vegetation type (fuel type in fire management language) on how many acres are burned on any given fire. They want to use the data to evaluate which areas to prioritize for cleaning, developing fire zones, and establishing fire prevention regulations. The agency has data from fires that occurred in 2018, and for each fire incident they have recorded total acres burned and the main vegetation type. The agency would like to figure out if more acres tend to get burned (higher risk of life and property loss) when the main vegetation type is herbaceous (grasses/brush) areas versus when the area is mostly wood (trees, shrubs).

At the 95% confidence level, do the data indicate that fires occurring at brush/grass vegetation areas tend to be more destructive fires than fires in wood areas? In this problem use a test statistic as part of the analysis leading to your result (not a confidence interval). (Data attached below.)

Please type up, show, and explain all work with equations. Thank you.

Incident #Vegetation typeAcres burned

1 Brush/Grass 6016

2 Brush/Grass 5824

3 Brush/Grass 5455

4 Brush/Grass 1819

5 Brush/Grass 3678

5 Brush/Grass 5865

6 Brush/Grass 3897

7 Brush/Grass 2771

8 Brush/Grass 4137

9 Brush/Grass 6566

10 Brush/Grass 5114

11 Brush/Grass 6066

12 Brush/Grass 4736

13 Brush/Grass 6360

14 Brush/Grass 2494

15 Brush/Grass 4656

16 Wood 3705

17 Wood 3346

18 Wood 4332

19 Wood 4780

20 Wood 3382

21 Wood 1672

22 Wood 2594

23 Wood 3729

24 Wood 3319

25 Wood 3827

26 Wood 2763

27 Wood 3009

28 Wood 2746