Question

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 255 items, 45 are defective. Calculate a 95.0% confidence interval estimate for the proportion of defectives from this production line. (Use 3 decimal places in calculations and in reporting your answers.)

Lower Limit:

Upper Limit:

Answer 1

lution :

Given that,

n = 255

x = 45

Point estimate = sample proportion = = x / n = 45/255=0.176

1 -   = 1- 0.176 =0.824

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.176*0.824) / 255)

= 0.047

A 95% confidence interval is ,

- E < p < + E

0.176-0.047 < p < 0.176+0.047

Lower Limit:0.129

Upper Limit:0.223