Answers : a) [74.0353,74.0367] b)[74.035, infinity) A manufacturer produces pist
ID: 2957624 • Letter: A
Question
Answers : a) [74.0353,74.0367] b)[74.035, infinity)
A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with sigma = 0.001 millimeters. A random sample of 15 rings has a mean diameter of x- = 74.036 millimeters. Construct a 99% two-sided confidence interval on the mean piston ring diameter. Construct a 99% lower-confidence bound on the mean piston ring diameter. Compare the lower bound of this confidence interval with the one in part (a).Explanation / Answer
a)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 74.036
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 0.001
n = sample size = 15
Thus,
Margin of Error E = 0.000665076
Lower bound = 74.03533492
Upper bound = 74.03666508
Thus, the confidence interval is
( 74.03533492 , 74.03666508 )
********************
b)
Note that
Lower Bound = X - z(alpha) * s / sqrt(n)
where
alpha = (1 - confidence level) = 0.05
X = sample mean = 74.036
z(alpha) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 0.001
n = sample size = 15
Thus,
Lower bound = 74.0355753
Thus, the confidence interval is u > 74.0356 [ANSWER]
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