A machine produces bearings with standard deviation of 0.2mm from the calibrated dimension of the inner diameter of a bearing. A quality control manager wants to test whether the machine was well calibrated for producing bearings with inner diameter of 32mm. A sample of 20 randomly chosen bearings has mean 31.9mm. Assume that the diameter of a randomly chosen bearing is normally distributed. Find the critical region of the test that the quality manager should perform and make a decision whether to reject Ho at the significance level 0.025. One of these may be useful. qnorm(0.025, mean=0, sd=1, lower.tail=FALSE) = 1.959964 qnorm(0.0125, mean=0, sd=1, lower.tail=FALSE) = 2.241403 qnorm(0.975, mean=0, sd=1, lower.tail=FALSE) = -1.959964 qnorm(0.9875, mean=0, sd=1, lower.tail=FALSE) = -2.241403 Which of the following answers is correct in all of its parts? sd-1, lower, tail Which of the following answers is correct in all of its parts? 2-32 O The critical region is the set C = (-00, -1.959964) and since the value of the test statistic is z = /v=-2.236068, we reject Ho: = 32 and conclude Ha: <32. i.e. that the machine is not calibrated for producing bearings with the inner diameter of 32mm. O The critical region is the set C = (-00, -2.241403) and since the value of the test =-2.236068, we accept Hoμ= 32 and conclude that the statistic is z = -32 machine is calibrated for producing bearings with the inner diameter of 32mm. O The critical region is the set C= = {z ER||z|> 1.959964} = (-00, -1.959964) U (1.959964, 00) and since -32 = -2.236068, we reject Ho: μ = 32 and the value of the test statistic is 2 = =1 conclude Haμ32, i.e. that the machine is not calibrated for producing bearings with the inner diameter of 32mm. The critical region is the set -32 C={zЄR||2| > 2.241403} = (-0, -2.241403) U (2.241403,∞) and since the value of the test statistic is z = =-2.236068, we fail to reject Hoμ = 32. That is, at the given significance level, there is not enough evidence to suggest that the machine is not well calibrated for producing bearings with the inner diameter of 32mm.
A machine produces bearings with standard deviation of 0.2mm from the calibrated dimension of the inner diameter of a bearing. A quality control manager wants to test whether the machine was well calibrated for producing bearings with inner diameter of 32mm. A sample of 20 randomly chosen bearings has mean 31.9mm. Assume that the diameter of a randomly chosen bearing is normally distributed. Find the critical region of the test that the quality manager should perform and make a decision whether to reject Ho at the significance level 0.025. One of these may be useful. qnorm(0.025, mean=0, sd=1, lower.tail=FALSE) = 1.959964 qnorm(0.0125, mean=0, sd=1, lower.tail=FALSE) = 2.241403 qnorm(0.975, mean=0, sd=1, lower.tail=FALSE) = -1.959964 qnorm(0.9875, mean=0, sd=1, lower.tail=FALSE) = -2.241403 Which of the following answers is correct in all of its parts? sd-1, lower, tail Which of the following answers is correct in all of its parts? 2-32 O The critical region is the set C = (-00, -1.959964) and since the value of the test statistic is z = /v=-2.236068, we reject Ho: = 32 and conclude Ha: <32. i.e. that the machine is not calibrated for producing bearings with the inner diameter of 32mm. O The critical region is the set C = (-00, -2.241403) and since the value of the test =-2.236068, we accept Hoμ= 32 and conclude that the statistic is z = -32 machine is calibrated for producing bearings with the inner diameter of 32mm. O The critical region is the set C= = {z ER||z|> 1.959964} = (-00, -1.959964) U (1.959964, 00) and since -32 = -2.236068, we reject Ho: μ = 32 and the value of the test statistic is 2 = =1 conclude Haμ32, i.e. that the machine is not calibrated for producing bearings with the inner diameter of 32mm. The critical region is the set -32 C={zЄR||2| > 2.241403} = (-0, -2.241403) U (2.241403,∞) and since the value of the test statistic is z = =-2.236068, we fail to reject Hoμ = 32. That is, at the given significance level, there is not enough evidence to suggest that the machine is not well calibrated for producing bearings with the inner diameter of 32mm.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A machine produces bearings with standard deviation of 0.2mm from the
calibrated dimension of the inner diameter of a bearing. A quality control manager
wants to test whether the machine was well calibrated for producing bearings with
inner diameter of 32mm. A sample of 20 randomly chosen bearings has mean
31.9mm. Assume that the diameter of a randomly chosen bearing is normally
distributed. Find the critical region of the test that the quality manager should
perform and make a decision whether to reject Ho at the significance level 0.025.
One of these may be useful.
qnorm(0.025, mean=0, sd=1, lower.tail=FALSE) = 1.959964
qnorm(0.0125, mean=0, sd=1, lower.tail=FALSE) = 2.241403
qnorm(0.975, mean=0, sd=1, lower.tail=FALSE) = -1.959964
qnorm(0.9875, mean=0, sd=1, lower.tail=FALSE) = -2.241403
Which of the following answers is correct in all of its parts?
Transcribed Image Text:sd-1, lower, tail
Which of the following answers is correct in all of its parts?
2-32
O The critical region is the set C = (-00, -1.959964) and since the value of the test
statistic is z =
/v=-2.236068, we reject Ho: = 32 and conclude Ha: <32.
i.e. that the machine is not calibrated for producing bearings with the inner diameter of
32mm.
O The critical region is the set C = (-00, -2.241403) and since the value of the test
=-2.236068, we accept Hoμ= 32 and conclude that the
statistic is z =
-32
machine is calibrated for producing bearings with the inner diameter of 32mm.
O The critical region is the set
C=
= {z ER||z|> 1.959964} = (-00, -1.959964) U (1.959964, 00) and since
-32 = -2.236068, we reject Ho: μ = 32 and
the value of the test statistic is 2 =
=1
conclude Haμ32, i.e. that the machine is not calibrated for producing bearings with
the inner diameter of 32mm.
The critical region is the set
-32
C={zЄR||2| > 2.241403} = (-0, -2.241403) U (2.241403,∞) and since
the value of the test statistic is z = =-2.236068, we fail to reject Hoμ = 32.
That is, at the given significance level, there is not enough evidence to suggest that the
machine is not well calibrated for producing bearings with the inner diameter of 32mm.
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