Mathematics 130 Chi Square Test For IndependenceName A number of fetal stem cell
ID: 2949296 • Letter: M
Question
Mathematics 130 Chi Square Test For IndependenceName A number of fetal stem cells may cross the placenta from the fetus to the mother during pregnancy and remain in the mother's tissue for decades. A recent study (2012) shows that the presence of fetal cells in the mother may offer protection against the onset of breast cancer Here is the matrix of the data: Women with onset Women without abels Brast Canccr Of breast canccr 140 women 250 women Lolums Women had fetal cells 400 women (01 Women had no fetal cells 200 women What are your informal observations about the onset ot breast cancer in women and the fetal stem cells found in the tissues of the mother Write At Least THREE complete sentences (oe ner as Ner mean to yo on words NCT THE Bcc Whot does ihe answer meonto you Apply the appropriate hypothesis test to the data. Write a COMPLETE ANSWER to the hypothesis test. In your entry for EXPLANATION explain clearly the informal observations that you have in ( # 1 ) .Explanation / Answer
(a)
(b)
Ho: presence of fetal cells and onset of breast cancer are independent.
Ha: presence of fetal cells and onset of breast cancer are not independent.
DF = (r - 1) * (c - 1) = (2 - 1) * (32- 1) = 1
Er,c = (nr * nc) / n
E1,1 = (540 * 390) / 990 = 212.73
E1,2 = (600 * 540) / 990 = 327.27
E2,1 = (390 * 450) / 990 = 177.27
E2,2 = (600 * 450) / 990 = 272.73
?2 = ? [ (Or,c - Er,c)2 / Er,c ]
?2 = (140 - 212.73)2/212.73 + (400 - 327.27)2/327.27 +
(250 - 177.27)2/177.27 + (200 - 272.73)2/272.73
?2 = 90.2564
The chi-square statistic is 90.2564.The P-Value is < 0.00001. The result is significant at p < 0.05.
Since the P-value (< 0.00001) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between presence of fetal cells and onset of breast cancer.
Breast cancer No breast cancer Marginal Row Totals fetal cells 140 (212.73) [24.86] 400 (327.27) [16.16] 540 no fetal cells 250 (177.27) [29.84] 200 (272.73) [19.39] 450 Marginal Column Totals 390 600 990 (Grand Total)