Question

on april 15, 1912, the rms titanic hit an iceberg and sank into the atlantic ocean. it was known that 40 percent of all people aboard the titanic were crew members. three hours later, the first three lifeboats were picked up by the carpathia. one of the ship’s officers felt that lifeboat boarding priority was given to passengers, so the surviving crew members were less than 40% of all survivors. based on the fact that 35 out of 125 people on those three lifeboats were crew members, test the officer’s claim. what are the null and alternative hypotheses? $h_0: p = 0.40$ and $h_a: p < 0.40$ $h_0: p \leq 0.40$ and $h_a: p > 0.40$ $h_0: p < 0.40$ and $h_a: p \geq 0.40$ none of the above

Explanation:

To determine the null and alternative hypotheses, we analyze the officer's claim. The null hypothesis ($H_0$) typically represents the status quo or no effect, while the alternative hypothesis ($H_a$) represents the claim we are testing. Here, the officer claims that the proportion of surviving crew members ($p$) is less than 40% (0.40). So, the null hypothesis assumes the proportion is equal to 0.40 (the original proportion of crew members aboard), and the alternative hypothesis is that the proportion is less than 0.40.

Answer:

A. $H_0: p = 0.40$ and $H_a: p < 0.40$