With the information shown, Please do step 3 & 4 of the hypothesis testing 1.The number of people who survived the Titanic based on class and sex is collected is collected in the table. Is there enough evidence to show that the class and the sex of a person who survived the Titanic are independent? 0.05 significance level. Null Hypothesis: class and sex of a person who survived the titanic are independent. Alternative Hypothesis: class and sex of a person who survived the titanic are dependent. The contingency table is: Class Male Female Total 1st 134 59 193 2nd 94 25 119 3rd 80 58 138 Total 308 142 450 Expected frequencies table is: Class Male Female Total 1st 193×308450=132.09 193×142450=60.90 193 2nd 119×308450=81.45 119×142450=37.55 119 3rd 138×308450=94.46 138×142450=43.55 138 Total 308 142 450 Conditions for the Chi-Square test for independence: Categorical Variables: The number of people who survived the titanic is divided based on sex and class. Therefore, the two categorical variables are sex and class. Categories: Sex and class are further divided into two and three categories: male and female for sex and 1st, 2nd, and 3rd for class. Independence of observation: Males of the 1st class are different from the male of the 2nd class. Similarly, the females of the 1st class are different from females of the 2nd class and so on. Relatively large sample: All the values of the expected frequencies in the table must be greater than 5. For this case, the required condition is satisfied.
With the information shown, Please do step 3 & 4 of the hypothesis testing
1.The number of people who survived the Titanic based on class and sex is collected is collected in the table. Is there enough evidence to show that the class and the sex of a person who survived the Titanic are independent? 0.05 significance level.
Null Hypothesis: class and sex of a person who survived the titanic are independent.
Alternative Hypothesis: class and sex of a person who survived the titanic are dependent.
- The
contingency table is:
|
Class |
Male |
Female |
Total |
|
1st |
134 |
59 |
193 |
|
2nd |
94 |
25 |
119 |
|
3rd |
80 |
58 |
138 |
|
Total |
308 |
142 |
450 |
Expected frequencies table is:
|
Class |
Male |
Female |
Total |
|
1st |
193×308450=132.09 |
193×142450=60.90 |
193 |
|
2nd |
119×308450=81.45 |
119×142450=37.55 |
119 |
|
3rd |
138×308450=94.46 |
138×142450=43.55 |
138 |
|
Total |
308 |
142 |
450 |
- Conditions for the Chi-Square test for independence:
Categorical Variables: The number of people who survived the titanic is divided based on sex and class. Therefore, the two categorical variables are sex and class.
Categories: Sex and class are further divided into two and three categories: male and female for sex and 1st, 2nd, and 3rd for class.
Independence of observation: Males of the 1st class are different from the male of the 2nd class. Similarly, the females of the 1st class are different from females of the 2nd class and so on.
Relatively large sample: All the values of the expected frequencies in the table must be greater than 5. For this case, the required condition is satisfied.
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