Question

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.

(a) 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 pound? Assume that σ is known to be 0.9 pound. (Round your answer up to the nearest integer.)

Answer 1

The minimum number of books that should be tested is 312.

Explanation:

The (1 - α)% confidence interval for population mean (μ) is:

`CI=\bar x\pm z_(\alpha/2)* (\sigma)/(√(n))`

The margin of error for this interval is:

`MOE= z_(\alpha/2)* (\sigma)/(√(n))`

The information provided is:

MOE = 0.10

σ = 0.90

Confidence level = 95%

Compute the critical value of z as follows:

`z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.96`

*Use a z-table.

Compute the value of n as follows:

`MOE= z_(\alpha/2)* (\sigma)/(√(n))`

`n=[(z_(\alpha/2)* \sigma)/(MOE) ]^(2)`

`=[(1.96* 0.90)/(0.10)]^(2)`

`=(17.64)^(2)\\=311.1696\\\approx312`

Thus, the minimum number of books that should be tested is 312.