Question

[14] In a random sample of 185 automobile engine crankshaft bearings, 18 had a defect. If this is an evidence that the true proportion of defective bearing is bigger than 6%, then we need to stop the production line for inspection. Calculate appropriate one-sided 95% confidence interval, and sate your conclusion.

Answer 1

H0: p <= 0.06

Ha: p > 0.06

Sample proportion $\hat{p}$ = 18 / 185 = 0.097

95% confidence interval is

= $\hat{p}$ + Z * sqrt( $\hat{p}$ ( 1 - $\hat{p}$) / N)

= 0.097 + 1.96 * Sqrt ( 0.097 * 0.903 / 185)

= 0.140

95% confidence interval is ( 0.140 , $\infty$)

Since claimed proportion 0.06 is not contained in confidence interval, reject the null hypothesis.

We conclude that we have sufficient evidence to support the claim.