Question

3.b). A jewelry artist has a new shipment of beads that she thinks are of lower quality than she expects from the supplier. To test this suspicion, she takes a random sample from her new stock of beads and finds that 21 beads out of 200 have under-sized holes. Find a 99% confidence interval for the proportion of beads that have under-sized holes.

Answer 1

Solution :

Given that,

n = 200

x = 21

Point estimate = sample proportion = = x / n = 21 /200=0.105

1 - = 1-0.105=0.895

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576 ( Using z table )

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

= 2.576 (((0.105*0.895) /200 )

E = 0.0558

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.105 -0.0558 < p <  0.105 +0.0558

0.0492< p < 0.1608

The 99% confidence interval for the population proportion p is : 0.0492, 0.1608