Question

19.13 In 1912, over 800 passengers perished after the ocean liner Titanic collided with an iceberg and sank. The table below compares the survival frequencies of cabin and steerage passengers. ACCOMMODATIONS ON THE TITANIC SURVIVED CABIN STEERAGE TOTAL YES 299 186 485 NO 280 526 806 TOTAL 712 1291 Source: Moca Dawson, RJ. (1995). The unusual episode data revisited. Journal of Statistical Education, 3, no. 3.

Answer 1

Step 1: Research Problem : Survival rates are independent of the passenger's accommodations (cabin or steer age) Step 2: Null hypothesis, Ho : Survival rates are independent of the passenger's accommodations (cabin or steer age) Step 3: Alternative hypothesis, HA: H, is not true. Step 4: degrees of freedom = (2-1)(2-1) = 1 Decision rule: We reject Ho at level 0.05 if calculated x > critical value where critical value = x2.0.5.1 = 3.8415

where critical value = X.05.1 = 3.8415 nad - bc)2 calculated x = (a + b)(c + d)(a + c) (6+ d) where, n = 1291, a = 299, c = 280, b = 186, d = 526 Step 5: Reject the null hypothesis at 5% level of significance. Step 6: Survival rates are not independent of the passenger's accommodations (cabin or steer age).

88.6488/1291 = 0.2620 > 0.25 strength of Cramer's V = V X2/n= relationship is very large. Odd ratio = ad = 3.0199