Managerial Report1. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p-value for each test.2. Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?3. Compute limits for the sample mean x around m = 12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x exceeds the upper limit or if x is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality control purposes.4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased? Sample 1Sample 2Sample 3Sample 411.5511.6211.9112.0211.6211.6911.3612.0211.5211.5911.7512.0511.7511.8211.9512.1811.9011.9712.1412.1111.6411.7111.7212.0711.8011.8711.6112.0512.0312.1011.8511.6411.9412.0112.1612.3911.9211.9911.9111.6512.1312.2012.1212.1112.0912.1611.6111.9011.9312.0012.2112.2212.2112.2811.5611.8812.3212.3911.9512.0311.9312.0012.0112.3511.8511.9212.0612.0911.7611.8311.7611.7712.1612.2311.8212.2011.7711.8412.1211.7912.0012.0711.6012.3012.0412.1111.9512.2711.9812.0511.9612.2912.3012.3712.2212.4712.1812.2511.7512.0311.9712.0411.9612.1712.1712.2411.9511.9411.8511.9211.8911.9712.3012.3711.8812.2312.1512.2211.9312.25 Quality Associates, Inc., a consulting firm, advises its clients about sampling andstatistical procedures that can be used to control their manufacturing processes.In one particular application, a client gave Quality Associates a sample of 800observations taken during a time in which that client's process was operatingsatisfactorily.The sample standard deviation for these data was .21; hence, with so much data, thepopulation standard deviation was assumed to be .21.• Quality Associates then suggested that random samples of size 30 be taken periodicallyto monitor the process on an ongoing basis.• By analyzing the new samples, the client could quickly learn whether the process wasoperating satisfactorily.When the process was not operating satisfactorily, corrective action could be taken toeliminate the problem.The design specification indicated the mean for the process should be 12.The hypothesis test suggested by Quality Associates follows.Hji jµ = 12H; µ # 12Corrective action will be taken any time Ho is rejected.The following samples were collected at hourly intervals during the first day of operationof the new statistical process control procedure. These data are available in the data setQuality.

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Description: Managerial Report1. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p-value for each test.2. Compute the standard deviation for each of the

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Managerial Report

1. Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be taken. Provide the test statistic and p-value for each test.

2. Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?

3. Compute limits for the sample mean x around m = 12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x exceeds the upper limit or if x is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality control purposes.

4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?

Sample 1
Sample 2
Sample 3
Sample 4
11.55
11.62
11.91
12.02
11.62
11.69
11.36
12.02
11.52
11.59
11.75
12.05
11.75
11.82
11.95
12.18
11.90
11.97
12.14
12.11
11.64
11.71
11.72
12.07
11.80
11.87
11.61
12.05
12.03
12.10
11.85
11.64
11.94
12.01
12.16
12.39
11.92
11.99
11.91
11.65
12.13
12.20
12.12
12.11
12.09
12.16
11.61
11.90
11.93
12.00
12.21
12.22
12.21
12.28
11.56
11.88
12.32
12.39
11.95
12.03
11.93
12.00
12.01
12.35
11.85
11.92
12.06
12.09
11.76
11.83
11.76
11.77
12.16
12.23
11.82
12.20
11.77
11.84
12.12
11.79
12.00
12.07
11.60
12.30
12.04
12.11
11.95
12.27
11.98
12.05
11.96
12.29
12.30
12.37
12.22
12.47
12.18
12.25
11.75
12.03
11.97
12.04
11.96
12.17
12.17
12.24
11.95
11.94
11.85
11.92
11.89
11.97
12.30
12.37
11.88
12.23
12.15
12.22
11.93
12.25

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 operating satisfactorily, corrective action could be taken to
eliminate the problem.
The design specification indicated the mean for the process should be 12.
The hypothesis test suggested by Quality Associates follows.
Hji jµ = 12
H; µ # 12
Corrective action will be taken any time Ho is rejected.
The following samples were collected at hourly intervals during the first day of operation
of the new statistical process control procedure. These data are available in the data set
Quality.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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