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It is known that roughly 5% of the general population carry a certain virus. A health researcher believes that among caucasian males the percentage is actually lower. Which of the following will provide the most convincing evidence to support the researcher’s suspicion? Out of 25 randomly chosen caucasian males, 1 male carries the virus. Out of 70 randomly chosen caucasian males, 3 males carry the virus. Out of 6,000 randomly chosen caucasian males, 288 males carry the virus. Out of 6,000 randomly chosen caucasian males, 240 males carry the virus.

Question

It is known that roughly 5% of the general population carry a certain virus. A health researcher believes that among caucasian males the percentage is actually lower. Which of the following will provide the most convincing evidence to support the researcher’s suspicion? Out of 25 randomly chosen caucasian males, 1 male carries the virus. Out of 70 randomly chosen caucasian males, 3 males carry the virus. Out of 6,000 randomly chosen caucasian males, 288 males carry the virus. Out of 6,000 randomly chosen caucasian males, 240 males carry the virus.

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Solution

To determine which scenario provides the most convincing evidence to support the researcher's suspicion, we need to calculate the percentage of Caucasian males carrying the virus in each scenario and compare it with the general population's 5%.

  1. In the first scenario, 1 out of 25 males carries the virus, which is 4% (1/25*100). This is lower than the general population's 5%.

  2. In the second scenario, 3 out of 70 males carry the virus, which is approximately 4.29% (3/70*100). This is also lower than the general population's 5%.

  3. In the third scenario, 288 out of 6,000 males carry the virus, which is 4.8% (288/6000*100). This is slightly lower than the general population's 5%.

  4. In the fourth scenario, 240 out of 6,000 males carry the virus, which is 4% (240/6000*100). This is lower than the general population's 5%.

While all scenarios show a lower percentage than the general population, the fourth scenario provides the most convincing evidence to support the researcher's suspicion. This is because it has the largest sample size (6,000 males) and the lowest percentage of virus carriers (4%). A larger sample size generally provides a more accurate estimate of the population parameter.

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