Final answer:
To estimate the average number of books Americans read per year with an 80% confidence level and a 0.77 margin of error, the required sample size is 90 subjects based on a population standard deviation of 5.7 books.
Step-by-step explanation:
To determine how many subjects are needed to estimate the average number of books Americans read with a margin of error of 0.77 books and an 80% confidence level, we use the formula for the sample size of a mean:
n = (Z*σ/E)^2
Where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level
- σ is the population standard deviation
- E is the margin of error
Given a population standard deviation (σ) of 5.7 books and a margin of error (E) of 0.77 books, we first need to find the Z-score for an 80% confidence level. For an 80% confidence level, the Z-score typically used is around 1.28.
Using the formula:
n = (1.28 * 5.7 / 0.77)^2
Calculating this, we find:
n = (7.296 / 0.77)^2
n = (9.4766)^2
n = 89.8179
The sample size should be the next whole number greater than the calculated value, since you can't have a fraction of a subject.
Therefore, you'll need 90 subjects to estimate the average number of books Americans read each year with a margin of error of 0.77 books with 80% confidence.