1 a and b please

1. Absurdly accomplished archaeologist and adventuress Arizona Ariel accesses any an- cient anteroom. The last 250 burial sites that Ari has investigated were guarded by four possible sets of nasty, poisonous critters: Spiders, Snakes, Spiders & Snakes, or Spiders, Snakes, & Scorpions. These sites were also guarded by man-made defenses of either bottomless pits, poisonous darts, or both. Ari's data tabulated below show the distribution for burial sites that she investigated. VENOMOUS CRITTERS MAN- SPIDERS, MADE SPIDERS SNAKES & PERILS SPIDERS SNAKES & SNAKES SCORPIONS TOTAL PITS 18 30 42 30 120 DARTS 20 8 36 16 80 BOTH 12 12 22 4 50 TOTAL 50 50 100 50 250 a. Do these data provide strong evidence at a = 0.04 that the Proportion of burial sites with all three critters is less than one-quarter? i. Test the Hypothesis that less than _ of tombs have all 3 critters. (40) ii. Find a comparable Confidence Interval for the Proportion of burial sites guarded by all 3 critters. (10) iii. Compare your Interval with your Test results. (10) b. Use these data to test at a = 0.02 the Hypotheses that: i. The ratio of man-made traps Pits:Darts:Both / 2:2:1 in burial sites, that is, their respective proportions are NOT 0.40, 0.40, and 0.20. (40) ii. There Is an association between the guardian critters (40) and man-made traps in burial sites. (140)