Amanufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 2%. a random sample of 250 lenses contains 6 defective lenses.
(a) formulate and test an appropriate set of hypotheses to determine whether the machine can be qualified. use α = 0.05. find the p-value.
(b) explain how the question in part (a) could be answered with a confidence interval. 9-97. a researcher claims th

Does not exceed 2% in both cases.

Step-by-step explanation:

Given that a  manufacturer of interocular lenses will qualify a new grinding machine if there is evidence that the percentage of polished lenses that contain surface defects does not exceed 2%.

Sample proportion =

Create hypothesses as

(Right tailed test at 5% significance level)

P difference = 0.004

Std error = 0.0089

test statistic Z = p diff/std error = 0.4518

p value = 0.326

Since p >alpha, we accept nullhypothesis

b) For confidence interval 97% we have

Margin of error = 2.17* std error = 0.0192

Confidence interval

=

Since 2% = 0.02 lies within this interval we accept null hypothesis.

Does not exceed 2%

Since

x/3-10=8

x/3=18

x=48