Answer:
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 = [tex]\frac{6}{250} \\=0.024[/tex]
Create hypothesses as
[tex]H_0: p = 0.02\\H_a : p >0.02[/tex]
(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
= [tex](0.024-0.0191, 0.024+0.0191)\\= (0.0049, 0.0431)\\[/tex]
Since 2% = 0.02 lies within this interval we accept null hypothesis.
Does not exceed 2%
Since