Chapter 26, Problem 23E

a)

To determine

To find the probability that we will draw a member of the crew.

Answer to Problem 23E

The probability that we will draw a member of the crew = 0.4021.

Explanation of Solution

Given:

  

Formula:

  $Probability=\frac{Numberofpossibleoutcomes}{Totalnumberofoutcomes.}$

The probability of crew is,

  $P(Crew)=\frac{885}{2201}=0.4021$

b)

To determine

To find the probability that third-class passenger who survived.

Answer to Problem 23E

The probability that third-class passenger who survived = 0.0809

Explanation of Solution

Given:

  

Formula:

  $Probability=\frac{Numberofpossibleoutcomes}{Totalnumberofoutcomes.}$

The probability that third-class passenger who survived is,

  $P(thirdand\text{alive})=\frac{178}{2201}=0.0809$

c)

To determine

To find the probability that selected passenger surviving given that the passenger was a first-class passenger.

Answer to Problem 23E

The probability that selected passenger surviving given that the passenger was a first-class passenger= 0.6215

Explanation of Solution

Given:

  

Formula:

  $Probability=\frac{Numberofpossibleoutcomes}{Totalnumberofoutcomes.}$

  $P(A|B)=\frac{P(A\cap B)}{P(B)}$

The probability that selected passenger surviving given that the passenger was a first-class passenger is,

  $P(\text{alive|First})=\frac{202}{325}=0.6215$

d)

To determine

To Find the number of members of the crew that expected to have lived.

Answer to Problem 23E

The expected number of members of the crew that expected to have lived = 285.4839.

Explanation of Solution

Given:

  

Formula:

  $Probability=\frac{Numberofpossibleoutcomes}{Totalnumberofoutcomes.}$

Expected value is E = np

First need to find probability of survived.

  $P(Alived)=\frac{710}{2201}=0.3226$

The expected number of members of the crew that expected to have lived are,

  $E=885\times 0.3226=285.4839$

e)

To determine

To state null and alternative hypotheses.

Answer to Problem 23E

  $H_0$ : Survival and class are independent.

  $H_a$ : Survival and class are not independent.

Explanation of Solution

Given:

  

The null and alternative hypotheses:

  $H_0$ : Survival and class are independent.

  $H_a$ : Survival and class are not independent.

f)

To determine

To find the degrees of freedom.

Answer to Problem 23E

The degrees of freedom = 3

Explanation of Solution

Given:

  

Formula:

  $df=(r-1)(c-1)$

The number of rows = r = 2

The number of columns = c = 4

Therefore, the degrees of freedom are:

  $df=(2-1)\times (4-1)=3$

g)

To determine

To state the conclusion.

Answer to Problem 23E

There is sufficient evidence to reject the claim of independence.

Explanation of Solution

Given:

  ${\chi }^2$ = 187.8

P-value = 0

Decision: The p-value< 0.05, reject H0.

Conclusion: There is sufficient evidence to reject the claim of independence.