Question

The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today.

Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer.

Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry. Make sure you include the 0 before the decimal.

Answer 1

Solution :

Given that,

n = 160

x = 14

Point estimate = sample proportion = = x / n = 14 / 160 = 0.088

1 - = 1 - 0.088 = 0.912

At 88% confidence level

= 1 - 88%

=1 - 0.88 =0.12

/2 = 0.06

Z/2 = Z0.06  = 1.555

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

= 1.555 (((0.088 * 0.912) / 160)

= 0.035

A 88% confidence interval for population proportion p is ,

± E   

= 0.088 ± 0.035

= ( 0.053, 0.123 )

LOWER limit = 0.053

UPPER limit = 0.123