We wish to conduct a survey to estimate the population, p, of individuals in the

Question

We wish to conduct a survey to estimate the population, p, of individuals in the population who have tested positive for HPV. A simple random sample of 1000 individuals is chosen. Each person is then Supplied with a coin and given the following instructions: Flip the coin in secret, if the coin comes up heads, answer question A below. If it comes up tails, answer question B. Q(A): To your knowledge, are you infected with HPV? Q(B): Is your zodiac sign included in of the following set? (cancer, leo, virgo) *of the 1000 sampled individuals, Suppose 170 responded "yes". a) How many peope are expecred to answer A and how many are expected to answer B? b) of the people who answered B, how many people would you expect to answer "yes"?

Explanation / Answer

(a)

Since the coin is fair, so out of the 1000 people, 500 are expected to answer A and 500 are expected to answer B.

(b)

Since there are 12 zodiac signs, so the probability that a person answering question B says yes is 3/12 = 0.25

So,

Expected number of people answering B who say yes = 500*0.25 = 125

(c)

Number of people answerig A who say yes = 170-125 = 45

So,

Estimate of the required population proportion = p = 45/500 = 0.09

Hope this helps !

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