Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was .21; hence, with so much data, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not
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What mistake or error could increase if the level of significance is increased?
Using Minitab, we obtain below information
One-Sample Z: Sample 1, Sample 2, Sample 3, Sample 4
Test of mu = 12 vs not = 12
The assumed standard deviation = 0.21
Variable N Mean StDev SE Mean 99% CI Z P
Sample 1 30 11.9587 0.2204 0.0383 (11.8599, 12.0574) -1.08 0.281
Sample 2 30 12.0287 0.2204 0.0383 (11.9299, 12.1274) 0.75 0.455
Sample 3 30 11.8890 0.2072 0.0383 (11.7902, 11.9878) -2.90 0.004
Sample 4 30 12.0813 0.2061 0.0383 (11.9826, 12.1801) 2.12 0.034 We conduct the hypotheses as follow:
H0: μ = 12 Ha: μ ≠ 12
As all sample number≥30, the sampling distribution of x ̅ can be approximated by a normal distribution. And we know from the case σ=0.21
Sample 1 x ̅_1=11.96, z1= -1.08, p-value=0.281>0.01, do not reject H0.
Sample 2 x ̅_2=12.03, z2= 0.75, p-value=0.455>0.01, do not reject H0.
Sample 3 x ̅_3=11.89, z3= -2.90, p-value=0.0040.01, do not reject H0.
We obtain from Minitab the sample standard deviation as follow:
S1=0.2204, S2=0.2204, S3=0.2072, S4=0.2061
We conduct the hypotheses as follow:
H0: σ=0.21 Ha: σ≠0.21
Sample 1 Sample 2
Sample 3 Sample 4 α = 0.01, df = 30 - 1 = 29 ,
With < < , we can not reject H0 and conclude the assumption of σ=0.21 for the population standard deviation appear reasonable.
We do not
What mistake or error could increase if the level of significance is increased?
Using Minitab, we obtain below information
One-Sample Z: Sample 1, Sample 2, Sample 3, Sample 4
Test of mu = 12 vs not = 12
The assumed standard deviation = 0.21
Variable N Mean StDev SE Mean 99% CI Z P
Sample 1 30 11.9587 0.2204 0.0383 (11.8599, 12.0574) -1.08 0.281
Sample 2 30 12.0287 0.2204 0.0383 (11.9299, 12.1274) 0.75 0.455
Sample 3 30 11.8890 0.2072 0.0383 (11.7902, 11.9878) -2.90 0.004
Sample 4 30 12.0813 0.2061 0.0383 (11.9826, 12.1801) 2.12 0.034 We conduct the hypotheses as follow:
H0: μ = 12 Ha: μ ≠ 12
As all sample number≥30, the sampling distribution of x ̅ can be approximated by a normal distribution. And we know from the case σ=0.21
Sample 1 x ̅_1=11.96, z1= -1.08, p-value=0.281>0.01, do not reject H0.
Sample 2 x ̅_2=12.03, z2= 0.75, p-value=0.455>0.01, do not reject H0.
Sample 3 x ̅_3=11.89, z3= -2.90, p-value=0.0040.01, do not reject H0.
We obtain from Minitab the sample standard deviation as follow:
S1=0.2204, S2=0.2204, S3=0.2072, S4=0.2061
We conduct the hypotheses as follow:
H0: σ=0.21 Ha: σ≠0.21
Sample 1 Sample 2
Sample 3 Sample 4 α = 0.01, df = 30 - 1 = 29 ,
With < < , we can not reject H0 and conclude the assumption of σ=0.21 for the population standard deviation appear reasonable.
We do not