Question

uppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 4 percentage points with 83% confidence

Answer 1

The answer is "294.2075".

Explanation:

Given:

`\hat{p} = 0.5 \\\\1 - \hat{p} = 1 - 0.5 = 0.5\\\\E = 4\% = 0.04\\\\`

At
`83\%` confidence level the z is ,

`\alpha = 1 - 83\% = 1 - 0.83 = 0.17\\\\(\alpha)/(2) = (0.17)/(2) = 0.085\\\\Z_{(\alpha)/(2)} = Z_(0.085) = 1.3722\\\\n = (\frac{Z_{(\alpha)/(2)}}{E})^2 * \hat{p} * (1 - \hat{p})\\\\`

`= ((1.3722)/(0.04))^2 * 0.5 * 0.5\\\\= (34.305)^2 * 0.5 * 0.5\\\\= 1,176.83 * 0.5 * 0.5\\\\= 1,176.83 * 0.25\\\\=294.2075`