Below is a table showing who survived the sinking of a ship based on whether the
ID: 3330568 • Letter: B
Question
Below
is a table showing who survived the sinking of a ship based on whether they were crew members, or passengers booked in first-, second-, or third-class staterooms.
1) If we draw an individual at random from this table, what's the probability that we will draw a member of the crew?
______%
2) What's the probability of randomly selecting a third-class passenger who survived?
______%
3) What's the probability of a randomly selected passenger surviving, given that the passenger was in a first class stateroom?
_______%
4) If someone's chances of surviving were the same regardless of their status on the ship, how many members of the crew would you expect to have lived?
______ crew members.
5) State the null and alternative hypotheses we would test here.
6) Give the degrees of freedom.
7) The chi-square value for the table is 178.6 and and the corresponding P-value is barely greater than 0.
State your conclusions about the hypotheses. Assume that 0.05 is a reasonable significance level.
is a table showing who survived the sinking of a ship based on whether they were crew members, or passengers booked in first-, second-, or third-class staterooms.
- Crew 1st 2nd 3rd Total Alive 211 201 100 221 733 Dead 668 107 248 431 1454 Total 879 308 348 652 2187Explanation / Answer
a) Probability that a randomly selected individual is a crew member is computed as:
= Total number of crew members / Total frequency
= 879 / 2187
= 0.402
Therefore 40.2% is the correct answer here.
b) Probability of randomly selecting a third class passenger who survived is computed as:
= Total number of third class passengers who survived / Total frequency
= 221 / 2187
= 0.101
Therefore 10.1% is the correct answer here.
c) Now given the passenger is I class passenger probability that the passenger survived is computed as:
= Number of I class passengers who survived / Total number of I class passengers
= 201 / 308
= 0.653
Therefore 65.3% is the correct answer here.
d) If the chances would have been same as to live or not, then the number of crew members who would be expected to live is computed as:
= Proportion of people who lived * Number of crew members
= ( 733 / 2187 ) * 879
= 294.61
Therefore approximately 295 crew members are expected to live.
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