A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a
particular binding machine. Strength can be measured by recording the force required to pull the pages of a
book from its binding.
If this force is measured in pounds, what is the minimum number of books that should be tested to
estimate the average force required to break the binding with a margin of error of 0.1 pounds with 95%
confidence? Assume that 𝜎 is known to be 0.7 pounds. (Round your answer up to the nearest integer.)
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To estimate the minimum number of books that should be tested, we can use the formula for the minimum sample size required for estimating a population mean with a specified margin of error.
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score for the desired confidence level (in this case, 95%, so Z = 1.96)
σ = standard deviation of the population (given as 0.7 pounds)
E = margin of error (0.1 pounds)
Plugging in the values:
n = (1.96 * 0.7 / 0.1)^2
n = (1.372 * 10)^2
n = 1.883^2
n = 3.54
Rounding up to the nearest integer, the minimum number of books that should be tested is 4.
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