Question

Question 2 12 pts Tick borne diseases are on the rise as ticks migrate to new areas of the United States. Historically, wildfire helped control tick populations. Researchers in the Southern U.S. decided to test the impact of fire on controlling the spread of lyme disease. Through coordination across several agencies, 5,000 acres of approximately contiguous forestland and rangeland is prescribe burned in late spring, with another adjacent, essentially identical 5,000 acres unburned. Over the next three years, ticks are collected at 200 sites on each tract of land to see if their tick abundance (ticks per acre) differs between tracts. hs a) State the null and alternative hypotheses for this problem using symbols (e.g., mu or p), not words. b) Several Routput summaries are given for analyzing the above data. Only one of the output summaries is correct for this scenario. Report the correct p-value and state the conclusion of the test. > t.test(burned, unburned, alternati ve="two.sided") Welch Two Sample t-test data: burned and unburned t = -2.1828, df = 245.38, p-value = 0.030486 alternative hypothesis: true differ ence in means is not equal to 0 95 percent confidence interval:

Answer 1

As we are checking if the tick abundance differ from the tracts, we need to conduct a two sided t test

> t.test(burned, unburned, alternat ve-"two.sided") Welch Two Sample t-test data: burned and unburned t = -2.1828, df = 245.38, p-value = 0.030486 alternative hypothesis: true diffe ence in means is not equal to 0 95 percent confidence interval: -15.91312 -12.20946 sample estimates: mean of x mean of y 7.63028 21.69157

$\small a)H_0:\mu_1=\mu_2,H_a:\mu_1\neq \mu_2$

b)pvalue=0.0305

At 5% level, we reject H0 and conclude that the tick abundance differ from the tracts.

c)There is a 3% probability that we might incorrectly reject the null hypothesis in favor of alternative

$\small d)CI=14.06129\pm1.96*\frac{4.322}{\sqrt{200}}=[13.4623, 14.6603 ]$

e)There is a 95% probability that the true mean of ticks per acre in the burned tract will be between 13.4623 and 14.6603