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a gallup poll wants to determine the mean number of books americans read each year. how many subjects are needed to estimate the average number of books americans read with a margin of error of 0.77 books with 80% confidence?initial results of the gallup poll indicate that the population standard deviation is 5.7 books.

User Yourstruly
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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.

User Mhenrixon
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