Question

A researcher asked individuals to disclose the number of books that they've read in the first half of 2020. Based on similar prior studies, a reasonable value for the standard deviation of these results is 8.3 books.

How many subjects are needed to estimate the average number of books that Americans have read in the first half of 2020 within 0.5 books with 95% confidence? (Round your answer up to the nearest integer)

Answer 1

Solution :

The sample size required to estimate the population mean at 95% confidence level is given as follows :

Where, Z_(0.05/2) is critical z-value at 95% confidence level, σ is population standard deviation and E is margin of error.

Since, we want to estimate the average number of books read within 0.5 books, therefore

Margin of error (E) = 0.5

σ = 8.3

Using Z-table we get, Z_(0.05/2) = 1.96

Hence, 1059 subjects are needed to estimate the average.

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