Question

Did the class of the passenger play a role in their survival during the sinking of the Titanic? The 1. data down represent the survival status of passengers by class of service Class Survived Did Not Survive First 223 152 Second 108 Third 128 328 a) b) Is the class of the passenger independent of survival status? Use a 10% significance level Identify the type of error that may have been committed.

Answer 1

Ho: Class of passenger and survival status are independent Hi Class of passenger and survival status are Not independent First SecondThirdTotal 223 Survived 128 328 456 459 657 108 Did not survive 152 Total 375 285 (Row Total) (Column Total) Grand Total We calculate expected frequencies by: E - Col-3 459 * 490 187.55 Col-1 Col-2 459* 459 375 1116 Row-1 154.23 1116 657285 1116 1116 657 *456 1116 Row-2657 375 220.77 167.78 268.45 1116 To calculate chi-square test statistic we calculate this formula on each cell (Observed Count - Expected Count)2 Expected Count Observed Count Expected Count (O - E)2 223 108 128 154.234 117.218 187.548 30.6598006 0.724863 18.907176

152 220.766 167.782 268.452 21.419864 0.506411 13.20912:3 85.427 243 328 2 - (O- E)2 Test statistic: X-S5.427 Significance level - 0.1 Degrees of freedom ,df - (r- 1) (c 1) (2-1) (3 1) 2 Critical value:4.605 X8.1 has area of 0.1 to its right. To find χ0.1 , open any Chi-square table, go across from ow df- -2 and doum from column 0.1 and get 4.605 To get p-value, we can use excel function CHÍSQ. DIST. RT( 85.427243 , 2) = 2.8165×10-19~0.0000 Since test statistic is greater than critical value , we (reject ) null hypothesis At 10% level, there is sufficient evidence that Class of passenger and survival status are not independent, i.e, that Class of passenger and survival status are significantly associated b) We may have rejected true null, and this is called type I error