To estimate the required sample size, we can use the formula for the sample size in a confidence interval estimation:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score (the value that corresponds to the desired confidence level, in this case, 90%)
σ = population standard deviation (15.5 books)
E = margin of error (1 book)
For a 90% confidence level, the Z-score is 1.645.
n = (1.645 * 15.5 / 1)^2
n ≈ (25.4975)^2
n ≈ 649.898
Since we cannot have a fraction of a subject, we round up to the nearest whole number.
n ≈ 650 subjects
Therefore, 650 subjects are needed to estimate the number of books read within one book with 90% confidence.
People were polled on how many books they read the previous year. How many subjects are needed to estimate the number of books read the previous year within one book with 90% confidence?
Initial survey results indicate that standard deviation= 15.5 books.
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