Question

A random sample of 200 printed circuits boards contains 15 defective or nonconforming units. Estimate the process fraction nonconforming. a. Test the hypothesis that the true fraction nonconforming in this process is 0.10. b. Construct a 95% confidence interval on the true fraction nonconforming in the production process.

Answer 1

a)

H0: p = 0.10

HA: p 0.10

Sample proportion = 15 / 200 = 0.075

Test statistics

z = - p / sqrt(p( 1 - p) / n)

= 0.075 - 0.10 / sqrt( 0.10 * 0.9 / 200)

= -1.18

This is test statistics value.

Critical value at 0.05 level = -1.96 , 1.96

Since test statistics value falls in the non-rejection region, that is falls between -1.96 and 1.96 ,

we do not have sufficient evidence to reject H0.

We conclude that we fail to support the claim.

b)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.075 - 1.96 * sqrt(0.075 * 0.925 / 200) < P < 0.075 + 1.96 * sqrt(0.075 * 0.925 / 200)

0.0385 < p < 0.1115

95% CI is ( 0.0385 , 0.1115)