Question

Question 5 of 10 (5 points) | Attempt 1 of 1 View question in a popup | 2h 53m Remaining 11.2 Section Exercise 14 (critical value, table) ol. Hurricane damage: In August and September 2005, Hurricanes Katrina and Rita caused extraordinary flooding in New Orleans, Louisiana. Many homes were severely damaged or destroyed, and of those that survived, many required extensive cleaning. It was thought that cleaning of flood-damaged homes might present a health hazard due to the large amounts of mold present in many of the homes. In a sample of 367 residents of Orleans Parish who had participated in cleaning of one or more homes, 81 had experienced symptoms of wheezing, and in a sample of 175 residents who had not participated in cleaning, 21 reported wheezing symptoms (numbers read from a graph). Can you conclude that there is a difference between the proportion of residents with wheezing symptoms who cleaned flood-damaged homes and those who did not participate in the cleaning? Let P1 denote the proportion of residents with wheezing symptoms who had cleaned flood-damaged homes, and let P, be the population proportion with wheezing symptoms who did not participate in the cleaning of flood-damaged homes. Use the a=0.01 level of significance and the critical value method. Part: 0 / 5 Part 1 of 5 State the null and alternate hypotheses. Next Part Submit Assignment

Answer 1

H₀: p1 = p2

H₁: p1 $\neq$ p2

$\widehat p1$ = 81/367 = 0.221

$\widehat p2$ = 21/175 = 0.12

The pooled sample proportion (P) = ($\widehat p1$ * n1 + $\widehat p2$ * n2)/(n1 + n2)

= (0.221 * 367 + 0.12 * 175)/(367 + 175)

= 0.1884

SE = sqrt(p(1 - p)(1/n1 + 1/n2))

= sqrt(0.1884 * (1 - 0.1884) * (1/367 + 1/175))

= 0.0359

The test statistic is

$z = \frac{\widehat p1 - \widehat p2}{SE}$

$= \frac{0.221 - 0.12}{0.0359}$

= 2.81

At $\alpha$ = 0.01, the critical values are +/- z_0.005 = +/- 2.58

Since the test statistic value is greater than the positive critical value (2.81 > 2.58), so we should reject the null hypothesis.

At 0.01 significance level, there is sufficient evidence to conclude that there is a difference between the proportion of residents with wheezing symptoms who cleaned flood-damaged homes and those who did not participate in the cleaning