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Questions 6鈥10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.


Men

Women

Boys

Girls

Survived

332

318

29

27

Died

1360

104

35

18

Given that the P-value for the hypothesis test is 0.000 when rounded to three decimal places, what do you conclude? What do the results indicate about the rule that women and children should be the first to be saved?

Short Answer

Expert verified

There is enough evidence to conclude that thesurvival of the passenger is not independent of whether he/she is a man, woman, boy or girl.

The rule to save women and children first seems to be applied here.

Step by step solution

01

Given information

A contingency table is constructed that shows the number of passengers who survived/died according to whether they were male, female, boy or girl.

02

Hypotheses

The null hypothesis is as follows:

The survival of the passenger is independent of whether he/she is a man, woman, boy or girl.

The alternative hypothesis is as follows:

The survival of the passenger is not independent of whether he/she is a man, woman, boy or girl.

03

P-value

The p-value is equal to 0.000.

The level of significance is equal to 0.05.

Since the p-value is less than 0.05, the null hypothesis is rejected.

There is enough evidence to conclude that thesurvival of the passenger is not independent of whether he/she is a man, woman, boy or girl.

04

Survival of a particular age group/gender

It is a rule that in times of calamities, the women and the children are saved first.

Here, since the survival of the passenger depends upon his/her age group and gender, it can be said that the above rule was followed at the time when the Titanic sank.

This also results in a large number of casualties for the male gender who are adults.

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Most popular questions from this chapter

Weather-Related Deaths For a recent year, the numbers of weather-related U.S. deaths for each month were 28, 17, 12, 24, 88, 61, 104, 32, 20, 13, 26, 25 (listed in order beginning with January). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Provide an explanation for the result.

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A study of people who refused to answer survey questions provided the randomly selected sample data shown in the table below (based on data from 鈥淚 Hear You Knocking But You Can鈥檛 Come In,鈥 by Fitzgerald and Fuller, Sociological Methods and Research,Vol. 11, No. 1). At the 0.01 significance level, test the claim that the cooperation of

the subject (response or refusal) is independent of the age category. Does any particular age group appear to be particularly uncooperative?

Age


18-21

22-29

30-39

40-49

50-59

60 and over

Responded

73

255

245

136

138

202

Refused

11

20

33

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27

49

Probability Refer to the results from the 150 subjects in Cumulative Review Exercise 5.

a.Find the probability that if 1 of the 150 subjects is randomly selected, the result is a woman who spent the money.

b.Find the probability that if 1 of the 150 subjects is randomly selected, the result is a woman who spent the money or was given a single 100-yuan bill.

c.If two different women are randomly selected, find the probability that they both spent the money.

Exercises 1鈥5 refer to the sample data in the following table, which summarizes the last digits of the heights (cm) of 300 randomly selected subjects (from Data Set 1 鈥淏ody Data鈥 in Appendix B). Assume that we want to use a 0.05 significance level to test the claim that the data are from a population having the property that the last digits are all equally likely.

Last Digit

0

1

2

3

4

5

6

7

8

9

Frequency

30

35

24

25

35

36

37

27

27

24

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

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