Question

A manufacturer randomly tests 150 items off of its assembly line and finds that 9 are defective. What is the lower bound for a 95% confidence interval for the proportion of all defective items produced of that assembly line? Round to at least 3 decimal places.

Answer 1

Solution :

Given that,

n = 150

x = 9

Point estimate = sample proportion = = x / n = 9 / 150 = 0.06

1 - = 1 - 0.06 = 0.94

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

Z   = Z _0.05 = 1.645

  Margin of error = E = Z * (( * (1 - )) / n)

= 1.645 * (((0.06 * 0.94 ) / 150)

= 0.032

A 95% Lower bound confidence interval for population proportion p is ,

- E

0.06 - 0.032 = 0.028

Lower bound = 0.028