Question

Studies show that 70% of people can get over the common cold in under a week. How many people must a doctor sample to be 90% confident of estimating the true proportion within a certain margin of error?

Answer 1

To be 90% confident of estimating the true proportion within a certain margin of error, a doctor must sample approximately 90 people.

Step-by-step explanation:

To determine how many people a doctor must sample in order to be 90% confident of estimating the true proportion within a certain margin of error, we can use the formula for sample size calculation:

Sample Size = (Z^2 * p * (1-p)) / E^2

Where:

• Z is the z-score corresponding to the desired level of confidence (in this case, 90% confidence level corresponds to a z-score of approximately 1.645)
• p is the estimated proportion (in this case, 70% or 0.7)
• E is the desired margin of error (for example, 0.05 or 5%)

Plugging in the values, we get:

Sample Size = (1.645^2 * 0.7 * (1 - 0.7)) / 0.05^2

Simplifying the equation, we find that the doctor must sample approximately 90 people to be 90% confident of estimating the true proportion within a certain margin of error.