Question

question 4
it is known that 4% of children carry a certain virus, but a leading health researcher suspects that the percentage is actually higher. which of the following provides the most convincing evidence to support the researcher’s suspicion?
select one answer.
10 points
a. out of 20 randomly chosen children, 1 child carries the virus.
b. out of 60 randomly chosen children, 3 children carry the virus.
c. out of 5,000 randomly chosen children, 250 children carry the virus.
d. out of 5,000 randomly chosen children, 210 children carry the virus.

Explanation:

Step1: Calculate the proportion for option A

The proportion of children carrying the virus in option A is $\frac{1}{20}=0.05 = 5\%$.

Step2: Calculate the proportion for option B

The proportion of children carrying the virus in option B is $\frac{3}{60}=0.05 = 5\%$.

Step3: Calculate the proportion for option C

The proportion of children carrying the virus in option C is $\frac{250}{5000}=0.05 = 5\%$.

Step4: Calculate the proportion for option D

The proportion of children carrying the virus in option D is $\frac{210}{5000}=0.042 = 4.2\%$.

Step5: Compare the proportions with the known 4%

Options A, B and C all have a proportion of 5% which is higher than 4%. Option D has a proportion of 4.2% which is also higher but less significantly. Among A, B and C, a larger sample size (5000 in option C) gives more reliable results.

Answer:

C. Out of 5,000 randomly chosen children, 250 children carry the virus.