In order to test whether the presence of fetal stem cells that have crossed the

Question

In order to test whether the presence of fetal stem cells that have crossed the placenta and remain in the woman's body have afforded some level of protection against the breast cancer, 54 women's will be the breast cancer and 45 who were cancer-free were examined. Fetal cells were present in 14 of the women with the breast cancer and in 25 of woman without. Test the hypothesis that the proportion p_1 of women with breast cancer whose bodies contain fetal stem cells is less than the proportion of p_2 of women without breast cancer whose bodies contain fetal stem cells, at the 1% level of significance, in the following series of steps. (The samples are sufficiently large to perform the test.) (a) State the null and the alternative hypotheses for the test. (b) State the formula for the test statistic and compute its value. Justify your answer. Construct the rejection region and make a decision.

Explanation / Answer

a)
Null hypothesis: P1 >= P2
Alternative hypothesis: P1 < P2

b)

p1 = 14/54 = 0.259, n1 = 54 , p2 = 25/45= 0.556, n2 =45
p = (p1 * n1 + p2 * n2) / (n1 + n2)
= [(0.259 * 54) + (0.556 * 45)] / (54 + 45)
= 0.394

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0.394 * 0.606 * ( 1/54 + 1/45 ) ]
= 0.0986

z = (p1 - p2) / SE
= (0.259 - 0.556)/0.0986
= -3.012

c) With alpha = .01 the critical z score is -2.33. We reject H0 if z < -2.33.

d) Here, z value is less than critical value
So, we reject the null hypothesis.

e) p value is calculated using z = -3.012
p value = 0.001298.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.