__STA2023 TEST 2 CHAPTERS 4, 10__

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- Using the Titanic mortality data in the table that follows:

** MEN WOMEN BOYS GIRLS**

**SURVIVED 332 318 29 27**

**DIED 1360 104 35 18**

Compute and show your work:

- If we randomly select someone who was aboard the Titanic, what is the probability to select a man?

- If we randomly select someone who was aboard the Titanic, what is the probability that died?

- If we randomly select someone who was aboard the Titanic, what is the probability that is a man who died?

- If we randomly select someone who was aboard the Titanic, what is the probability that is either a man or a dead person?

- If we randomly select someone who was aboard the Titanic, what is the probability that person is a man, given that he died?

- If we randomly select someone who was aboard the Titanic, what is the probability that is not a man?

- Are the events to be a man and to die mutually exclusive? Why?

- Are the events to be a man and to die independents? Why?

- Compute how many committees of 5 senators consisting in 3 democrats and 2 republicans you can draw from a senate serving with 51 senators democrats and 49 senators republicans.

- Compute the probability to draw a poker hand with all red cards from a standard card deck

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**Interpret the following MINITAB displays:**

1) Data sodium

2.30 2.60 2.34 2.40 2.50 2.45 2.35 2.60 2.36 2.42 2.50 2.30 2.53

2.57 2.62 2.53 2.54 2.62

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**3) Correlation: Data sodium, Body weight **

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Pearson correlation of Data sodium and Body weight = 0.576

P-Value = 0.012

**4) Regression Analysis: Body weight versus Data sodium **

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The regression equation is

Body weight = 49.06 + 10.10 Data sodium

S = 1.64626 R-Sq = 33.2% R-Sq(adj) = 29.1%

Analysis of Variance

Source DF SS MS F P

Regression 1 21.5817 21.5817 7.96 0.012

Error 16 43.3627 2.7102

Total 17 64.9444

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**5) Chi-Square Test for Association: Ethnicity, Gender **

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Rows: Ethnicity Columns: Gender

F M All

A 1 2 3

1.500 1.500

0.1667 0.1667

B 2 2 4

2.000 2.000

0.0000 0.0000

C 1 1 2

1.000 1.000

0.0000 0.0000

H 3 4 7

3.500 3.500

0.0714 0.0714

N 2 0 2

1.000 1.000

1.0000 1.0000

All 9 9 18

Cell Contents: Count

Expected count

Contribution to Chi-square

Pearson Chi-Square = 2.476, DF = 4, P-Value = 0.649

Likelihood Ratio Chi-Square = 3.256, DF = 4, P-Value = 0.516

* NOTE * 10 cells with expected counts less than 5