Question

In a random sample of 80 automobile engine crankshaft bearings, 8 have a surface finish that is rougher than specifications allow. Find a 99% confidence interval for ?, the population proportion of crankshaft bearings that have a surface finish that is rougher than specifications allow.

Answer 1

Point estimate = sample proportion = = x / n = 8 / 80 = 0.10

Z_/2 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.10 * 0.90) / 80)

= 0.086

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.10 - 0.086 < p < 0.10 + 0.086

0.014 < p < 0.186

(0.014 , 0.186)