Question

How many samples should we collect for the following scenario? We want to know the proportion of students who were sick at least one time during the semester with the level of precision (4%) and 95 percent confidence level (i.e., the corresponding z=1.96) assuming the estimated proportion is 0.5. Round up your answer to the integer.

Answer 1

To estimate the proportion, you need a sample size of 601 students.

Step-by-step explanation:

To determine the number of samples needed to estimate the proportion of students who were sick at least one time during the semester with a precision of 4% and a 95% confidence level, you can use the formula:

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

where:

• n is the required sample size
• Z is the Z-value corresponding to the desired confidence level (1.96 for 95% confidence)
• p is the estimated proportion (0.5)
• E is the desired precision (0.04)

Substituting these values into the formula gives:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.04^2)

n = 600.25

Since the sample size must be an integer, round up the result to the nearest whole number:

n = 601