neering Statistics 2104223 Ex: Cancer 14 Early Detection of Breast Cancer Of tho

Question

neering Statistics 2104223 Ex: Cancer 14 Early Detection of Breast Cancer Of those women who are diagnosed to have early-stage breast cancer, one third eventually die of the disease. Suppose a community public health department instituted a screening program to provide of the early detection of breast cancer and to increase the survival rate p of those diagnosed to have the disease. A random sample of 200 women was selected from among those who were periodically screened by the program and who were diagnosed to have the disease. Let X represent the number of those in the sample who survive the disease. If 164 women in the sample of 200 survive the disease, can you conclude that the community screening program was effective? Test using -05 and explain the practical conclusions from your test. Find the p-value for the test and interpret it. 59 871-880 250

Explanation / Answer

here we are given that

p0 = 1/3 = 0.33 = 1-0.33 = 0.66 , suvived
phat = 164/200 = 0.82

we know that the z test for porportion is given as

Z = (phat - p0)/sqrt(p0*(1-p0)/n)

= (0.82-0.66)/sqrt(0.66*(1-0.66)/200)
= 3.91

now we check the z table for the p value as

P ( Z>3.91 )=1P ( Z<3.91 )=11=0

as the p value is less than 0.05 , hence we can conclude that the survival rate has significantly increased due to the program

H0 : survival rate did not increase due to the program
H1 : survival rate has significantly increased due to the program

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