Question

question 3
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 researchers suspicion?
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 each option

Option A:

The proportion of children with the virus is $\frac{1}{20}=0.05 = 5\%$.

Option B:

The proportion is $\frac{3}{60}=0.05 = 5\%$.

Option C:

The proportion is $\frac{250}{5000}=0.05 = 5\%$.

Option D:

The proportion is $\frac{210}{5000}=0.042 = 4.2\%$.

Step2: Compare with the known rate

The known rate is $4\%$. Options A, B and C have proportions of $5\%$ which are higher than $4\%$, while option D has a proportion close to $4\%$. Also, a larger sample size (5000 in options C and D compared to 20 and 60 in options A and B) gives more reliable results. Among the options with higher - than - 4% proportions and large sample size, we consider the significance. A larger deviation from the known rate in a large sample is more convincing.

Answer:

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