We wish to conduct a survey to estimate the proportion, p, of individuals in the
ID: 3028285 • Letter: W
Question
We wish to conduct a survey to estimate the proportion, 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. To you knowledge, are you infected with HPV? Is your zodiac sign included in the following set? (Cancer, Leo, Virgo) How many people would expect to answer A, and how many would you expect to answer B? Of the people who answered B, how many people would you expect to answer -yes-? Using you answer to (b) estimate the percentage, p, of people in the population that are carriers of HPV and are aware of their condition? What type of bias is this type of question design aiming to mitigate?Explanation / Answer
A simple random sample of 1000 individuals is chosen.
a) As a coin is flipped and (as each head and tail is equally likely) so the probability of being a head is 0.5 and tail is 0.5, so the number of people expected to answer A is 1000 x 0.5 =500, and similarly, the number of people expected to answer B is 1000 x 0.5 =500.
b) Since the number of zodiac sign are 12, so the probability of having zodiac sign from the set (Cancer, Leo, Virgo) is 3/12=1/4=0.25. So out of the number of people who answered B, that is 500, the number of people expected who would answer "yes" is 500 x 0.25 =125.
c) So the percentage p, of people that are carriers of HPV and are aware of their conditions can not be confirmed from this information.
d) Here the questions asked were redundant and inconclusive, and thus do not give any conclusion regarding the proportion of poulation who have tested poitive.
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