Part 6: Quantitative Methods and Tools Flashcards
A project is being conducted in a hospital clinic. Which of the following is not considered discrete data?
A) Patient weight
B) Result of a pass/fail medical test
C) Error in a medical record
D) Number of patient visits
A) Patient Weight
A projected is being conducted in a manufacturing facility. Which of the following is not considered continuous data?
A) The length of a component
B) Fill volume of a container
C) Number of nonconforming components
D) Time required for testing
C) Number of nonconforming components
The color of a car is on which measurement scale?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
A) Nominal
A person’s height in feet is on which measurement scale?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
D) Ratio
The rating of a service from poor to excellent is on which measurement scale?
A) Nominal
B) Ordinal
C) Interval
D) Ratio
B) Ordinal
A research team is doing a study of students at a college and would like to ensure that their sample has all four levels of students: freshmen, sophomores, juniors, and seniors. What sampling method is most appropriate for this study?
A) Double sampling
B) Stratified sampling
C) Simple random sampling
D) Multiple sampling
B) Stratified sampling
The waiting times in minutes for eight customers at a bank are: 5, 8, 12, 3, 2, 7, 6, 5. What are the mean and median for this sample of waiting times?
A) Xbar = 5.5 min, M = 6 min
B) Xbar = 6 min, M = 5 min
C) Xbar = 6 min, M = 5.5 min
D) Xbar = 6 min, M = 6 min
C) Xbar= 6 min, M = 5.5 min
The lengths in inches for a sample of seven components are: 3.2, 3.1, 3.4, 3.1, 3.2, 3.3, 3.2. What is the standard deviation for this sample?
A) s = 0.1069 in
B) s = 0.0114 in
C) s = 0.0098 in
D) s = 0.0989 in
A) s = 0.1069 in
The median of a population is much larger than the population mean. What can you say about the shape of the population distribution?
A) The distribution is symmetric
B) The distribution is right skewed
C) The distribution is left skewed
D) None of the above
C) The distribution is left skewed
A population has an exponential distribution. One hundred samples of size 40 are randomly collected and the 100 sample means are calculated. What is the approximate distribution of these sample averages?
A) Binomial
B) Normal
C) Uniform
D) Poisson
B) Normal
What is the formula for the population variance?
A) sum of (sample - population mean) / Population
B) sum of (sample - sample mean)^2 / (Sample population - 1)
C) sum of (sample - population mean)^2 / Population
D) sum of (sample - population mean)^2 / (Population - 1)
C) sum of (sample - population mean)^2 / Population
Σ (x-μ)^2 / N
A team would like to compare waiting times of customer by day of the week. Which of the following would be the most appropriate tool to use?
A) Histograms
B) Box plots
C) Scatter plots
D) Probability plots
B) Box plots
Which of the following descriptive statistics is not typically found in a box plot?
A) Minimum
B) Maximum
C) Mean
D) Median
C) Mean
Which of the following is an advantage of a stem and leaf plot compared to a histogram?
A) Stem and leaf plots contain more information than a histogram
B) Stem and leaf plots provide a depiction of the shape of the data
C) Stem and leaf plots provide a time reference
D) None of the above
A) Stem and leaf plots contain more information than a histogram
A team measured the time to failure of 20 components. They plotted the data in a normal probability plot (Page 95). What conclusions can be drawn?
A) The normal distribution is not a reasonable model for the time to failure
B) The Weibull distribution is a reasonable model for the time to failure
C) The normal distribution is a reasonable model for the time to failure
D) Not enough information provided to draw conclusions.
A) The normal distribution is not a reasonable model for the time to failure
The temperature of coffee is an important characteristic in a restaurant. The temperature of 15 randomly selected cups of coffee is measured and the average temperature is found to be 168°F. Which term best describes this average temperature?
A) Population
B) Sample
C) Parameter
D) Statistic
D) Statistic
A characteristic of a population is called a:
A) Sample
B) Statistic
C) Parameter
D) Probability
C) Parameter
The contingency table below describes the relationship between the number of nonconforming components produced and time of day.
Time Conforming Qty Nonconforming Qty
Day 94 5
Evening 87 10
Overnight 65 23
Totals 246 38
Given that a part is made overnight, what is the probability it is nonconforming?
A) 0.08
B) 0.61
C) 0.43
D) 0.26
D) 0.26
The probability of a part being defective is 0.02. What is the probability it is not defective?
A) 0.88
B) 0.98
C) 1.08
D) 2%
B) 0.98
The probability that event A occurs is 0.72. The probability that event B occurs is 0.03. What is the probability that events A and B both occur?
A) 0.0216
B) 0.75
C) 0.69
D) Not enough information provided
D) Not enough information
If the probability that event A occurs is 0.40, the probability that event B occurs is 0.13, and A and B are mutually exclusive events, what is the probability that events A and B both occur?
A) 0
B) 0.052
C) 0.53
D) 1.27
A) 0
The time between arrivals at a store has an exponential distribution with mean five minutes. What is the probability that the time between arrivals is less than three minutes?
A) 0.9999
B) 0
C) 0.5488
D) 0.4512
D) 0.4512
X has a normal distribution with mean 15 and standard deviation 2. What is the probability that X is greater than 18?
A) 0.0668
B) 0.8554
C) 0.9332
D) 0.1446
A) 0.0668
Which of the following probability distributions is not symmetric?
A) Normal
B) t
C) Uniform
D) None of the above
D) None of the above
A bottling company’s filling process has a normal distribution with mean 24.01 oz and standard deviation of 0.025 oz. If the specifications for the process are 24 +/- 0.08 oz, what proportion of bottles is overfilled?
A) 0.99488
B) 0.00256
C) 0.99744
D) 0.00016
B) 0.00256
Compared to the standard normal distribution, the Student’s t-distribution:
A) has a larger mean
B) is more skewed to the right
C) is bimodal
D) Has heavier tails
D) Has heavier tails
The number of nonconformities per inspection unit in a factory occurs at a rate of 5 per day. Using the most appropriate probability distribution, what is the probability there will be at least two nonconforming units in one day?
A) 0.0404
B) 0.2627
C) 0.9596
D) 0.8000
C) 0.9596
A sample of 10 products is selected from a small, isolated lot without replacement. The lot is known to contain 5% defective products. Which distribution is most appropriate to determine the probability of selecting at least one defective item in the sample?
A) Hypergeometric
B) Binomial
C) Poisson
D) Normal
A) Hypergeometric
Fifteen invoices are randomly selected from a batch at a company. It is believed that 10% of all invoices have an error. What is the probability that exactly four out of the 15 invoices have an error?
A) 0.0428
B) 0.9873
C) 0.0127
D) 1.0421
A) 0.0428
Suppose the number of errors in an invoice at a company has the probability mass function (written in table form) shown. What is the expected number of errors in a randomly selected invoice?
# of errors 0 1 2 3 4 Probability 0.86 0.06 0.04 0.03 0.01
A) 0.27
B) 0.5771
C) 0.7597
D) 0
A) 0.27
A population has a distribution with mean 24 and standard deviation 5.5 oz. According to the central limit theorem, what is the mean of the distribution of the sample means for random samples of size 32?
A) 24 / 5.5
B) 24 / 32
C) 24
D) 24 / sqrt(32)
C) 24
A bottling company’s filling process has a normal distribution with mean 24 oz and standard deviation 0.05 oz. What is the probability that a sample of 16 randomly selected bottles will have an average volume more than 24.04 oz?
A) 0.9993
B) 0.0007
C) 0.2119
D) 0
B) 0.0007
A sample of size 16 is drawn from a population that follows a normal distribution with mean 58 and variance 64. What is the standard error of the sample mean?
A) 8
B) 2
C) 16
D) 4
B) 2
The 95% confidence interval for the proportion of filing errors in a business is (0.02, 0.12). What conclusions can be drawn from this confidence interval?
A) There is a 95% chance that the population proportion p is between 0.02 and 0.12
B) The probability that the confidence interval contains the population proportions p is 0 or 1
C) We are 95% confident that the confidence interval will contain the population proportion p.
D) b and c
E) All of the above
D) b and c
A team would like to estimate the average length of a component. A random sample of 50 components had a sample mean of 11.75 mm. Which of the following terms is used to describe this value?
A) Point estimate
B) Parameter
C) Probability
D) Standard error
A) Point estimate
The tensile strength of 15 units of cement was tested. The sample mean tensile strength was 4.3MPa and sample standard deviation was 0.51MPa. Find a 99% confidence interval for the true mean tensile strength of the cement.
A) (4.018, 4.582)
B) (2.782, 5.818)
C) (3.961, 4.639)
D) (3.908, 4.692)
D) (3.908, 4.692)
A team would like to estimate the true average tensile strength of cement. They would like to obtain an estimate within 0.15 MPa of the true average tensile strength with 95% confidence. Based on prior information, it is assumed that σ = 0.50 MPa. What sample size is required to meet these requirements?
A) 43
B) 42
C) 6
D) 7
A) 43
The voltage of a power supply is of interest to a team. Voltage is assumed to be normally distributed. The voltages of seven randomly selected observations are: 10.37, 11.50, 9.80, 10.65, 10.15, 9.52. Find the 95% confidence interval of the population variance of voltage.
A) (9.745, 11.380)
B) (0.570, 1.946)
C) (0.378, 4.419)
D) (0.324, 3.788)
D) (0.324, 3.788)
A bottling factory claims that the volume of soda filled in bottles is 18oz. You want to test whether the true mean volume of soda is different than 18oz. The volume of a random sample of 24 bottles had a mean of 17.98 oz with a standard deviation of 0.03 oz. Using a significance level of 5%, what is the appropriate test statistic for this hypothesis test.
A) 3.266
B) 2.069
C) -3.266
D) -0.667
C) -3.266
A bottling factory claims that the volume of soda filled in bottles is 18oz. You want to test whether the true mean volume of soda is different than 18oz. The volume of a random sample of 24 bottles had a mean of 17.98 oz with a standard deviation of 0.003 oz. Using a significance level of 5%, what conclusions can be made.
A) There is not sufficient evidence to conclude that the mean volume is different than 18oz.
B) There is sufficient evidence to conclude that the mean volume is different than 18oz.
C) 18 would be contain in a 95% confidence interval of the population mean.
D) None of the above
B) There is sufficient evidence to conclude that the mean volume is different than 18oz.
Speed bumps were installed in a neighborhood to slow traffic. After installation, the speed after the last speed bump of a random sample of 20 cars were recorded. The mean speed was 24.50 mph and the standard deviation was 2.3 mph. The team wanted to determine if the average speed is less than 25mph. What are the appropriate hypothesis for this hypothesis test?
A) H(null): μ = 25 vs H(a): μ ≠ 25
B) H(null): μ > 25 vs H(a): μ = 25
C) H(null): μ = 25 vs H(a): μ < 25
D) H(null): μ = 25 vs H(a): μ > 25
C) H(null): μ = 25 vs H(a): μ < 25
A team investigated the number of patient falls in a hospital. 56 patients were randomly selected. Out of the 56 patients, there were six recorded patient falls. The hospital wanted to determine whether the proportion of patient falls was more than 10 %. At the 5% significance level, what is your conclusion to this hypothesis test?
A) Reject H(null), conclude that the proportion of patient falls equals 0.10
B) Reject H(null), conclude that the proportion of patient falls is more than 0.10
C) Do not reject H(null) conclude that the proportion of patient falls equals 0.10
D) Do not reject H(null), conclude that the proportion of patient falls is more than 0.10
C) Do not reject H(null) conclude that the proportion of patient falls equals 0.10
Two methods for filling a bottle are being compared at a factory. The 90% confidence interval for the difference in volume for two independent random samples of the filling methods was found to be (-0.091, -0.049). Based on this confidence interval, is there evidence that the two filling methods are different?
A) Yes, since 0 is not in the confidence interval
B) Yes, since 0 is in the confidence interval
C) No, since 0 is not in the confidence interval
D) No, since 0 is in the confidence interval
A) Yes, since 0 is not in the confidence interval
An improvement project was done at a factory to decrease packaging time. The following data were collected before and after the improvement project:
Before: Sample mean - 3.52, Sample variance - 2.34, Sample size = 28
After: Sample mean - 2.10, Sample variance - 2.04, Sample size = 25
A hypothesis test was performed with H(null): μ(before) - μ(after) = 0. What is the critical value for this hypothesis test (Use α = 0.01)?
A) -2.403
B) 2.403
C) 2.678
D) 2.576
B) 2.403
An improvement project was done at a factory to decrease packaging time. The following data were collected before and after the improvement project:
Before: Sample mean - 3.52, Sample variance - 2.34, Sample size = 28
After: Sample mean - 2.10, Sample variance - 2.04, Sample size = 25
The project team would like to determine whether the variance of packaging time has changed at the 10% significance level. What is the test statistic for the appropriate hypothesis test?
A) 1.071
B) 3.494
C) 1.930
D) 1.147
D) 1.147
Two machines product the same parts. A random sample of 1250 parts from machine 1 has 28 that are nonconforming, and a random sample of 1175 parts from machine 2 has 18 that are nonconforming. Find the 90% confidence interval for the difference between the proportions of nonconforming parts form machine 1 and 2.
A) (-0.002, 0.016)
B) (-0.004, 0.018)
C) (0, 0.016)
D) (0.006, 0.008)
A) (-0.002, 0.016)
A hypothesis test is performed at the 10% significance level. The power of the test is 0.80, or 80%. What is the type II error for this hypothesis test?
A) 0.90
B) 0.10
C) 0.80
D) 0.20
D) 0.20
When the null hypothesis is not rejected when in fact the null hypothesis is false, what type of error has been made?
A) Sampling error
B) Type I error
C) Type II error
D) No error has been made
C) Type II error
A team would like to compare the proportion of defective widgets produced by two machines. What distribution does the test statistic for this hypothesis test follow?
A) Normal
B) t
C) Poisson
D) Uniform
A) Normal
The heart rates of 12 individuals were measured using two different pieces of equipment. A team would like to compare the measure heart rates of the two pieces of equipment. Which hypothesis test would be most appropriate?
A) Paired t-test
B) Two-sample t-test
C) Two-sample p-test
D) Goodness of fit test
A) Paired t-test
The length of five components was measred by two inspectors (data shown below). Assuming the data follow a normal distribution, what ist eh test statistic for the appropriate hypothesis test for this scenario? Use α = 0.01
Component 1 2 3 4 5
Inspector A 10.2 9.8 10.1 10.3 10.4
Inspector B 10.0 9.9 10.3 10.0 10.3
A) 2.576
B) 0.65
C) 0.45
D) 4.604
B) 0.65
A team at a hospital did a project on medication errors. A random sample of medication errors yilded the following results:
Type of error Number of errors Incorrect dose 32 Wrong dose 28 Incorrect form 45 Wrong amount 35 Total 140
The team would like to test the hypothesis at the 5% significance level that the medication error occur with equal probabilities. What is the value of the test statistic for this hypothesis test?
A) 7.815
B) 1.96
C) 0
D) 4.514
D) 4.514
What distribution does the test statistic use in the goodness-of-fit test follow?
A) t
B) chi-square
C) F
D) Normal
B) chi-square
A study was done to compare the elasticity of a polymer mortar during a compression test at three different strain rates. Below is the ANOVA table for the statistical analysis. What is your conclusion at the 5% significance level?
Source dF SS MS F
Strain rate 2 0.1614 0.0807 1.70
Error 12 0.5688 0.0474
Total 14 0.7302
A) Reject H(null), conclude that the three means are the same
B) Reject H(null), conclude that at least one mean is different than the others
C) Do not reject H(null), conclude that the three means are the same
D) Do not reject H(null), conclude that at least one man is different than the others.
C) Do not reject H(null), conclude that the three means are the same
Which of the following is not an assumption required for use and interpretation of a one-way ANOVA?
A) Homogeneity of variance
B) Observations are paired
C) Observations are independent
D) Observations are normally distributed
B) Observations are paired
A two way ANOVA hypothesis test was used to test the effects of two factors on a response variable. What conclusions can be made from the interaction plot on page 105?
A) High levels of factor B tend to have smaller response values
B) There is not an interaction effect between factors A and B.
C) There is an interaction effect between factors A and B.
D) Factors A and B do not have an effect on the response variable
B) There is not an interaction effect between factors A and B.
Consider the contingency table presented below. A hypothesis test for independence is conducted to determine if the number of nonconforming parts produced is independent of time of day. What type of distribution does the test statistic for this hypothesis test have?
Time Good parts Bad parts Totals
Day 94 5 99
Evening 87 10 97
Overnight 65 23 88
Totals 246 38 284
A) x^2
B) Normal
C) Binomial
D) Poisson
A) x^2
The value of the test statistic for the hypothesis test is 19.040. What is the conclusion from this hypothesis test (use α = 0.05)?
Time Good parts Bad parts Totals
Day 94 5 99
Evening 87 10 97
Overnight 65 23 88
Totals 246 38 284
A) Reject H(null) conclude that type of parts produced and time of day are independent
B) Reject H(null), conclude that typed of parts produced and time of day are not independent.
C) Do not reject H(null), conclude that type of parts produced and time of day are independent
D) Do not reject H(null), conclude that type of parts produced and time of day are not independent.
B) Reject H(null), conclude that typed of parts produced and time of day are not independent.
The fitted regression equation for two variable s x and y is y’ = 2.5x-8. What is the slope of this equation?
A) -8
B) 1
C) 2.5
D) 0.89
C) 2.5
A team wants to predict a person’s cholesterol based on their weight in pounds. The fitted regression equation is Cholesterol = 140 + 0.23 X Weight. What is the predicted cholesterol of a person who weighs 130 pounds?
A) 169.9
B) 140
C) 0.23
D) 162.2
A) 169.9
Paired data collected from a process are: (5.2, 26.7), (6.1, 27.5), (3.2, 24.9), (4.6, 25.5). What is the slope of the linear regression equation for these data?
A) 0.92
B) 0.96
C) 21.74
D) -0.92
A) 0.92
A study was done to predict people’s cholesterol by their weight. A sample of 21 people was collected, and the linear regression equation was found to be Cholesterol = 140 + 0.20 X Weight. The team would like to determine if there is a significant linear relationship between weight and cholesterol. What is the appropriate alternative hypothesis for this statistical test?
A) H(a): β(1) = 0
B) H(a): β(0) = 0
C) H(a): β(1) ≠ 0
D) H(a): β(0) ≠ 0
C) H(a): β(1) ≠ 0
The scatter plot on page 107 displays the relationship between two random variables. What is the correlation coefficient of these two variables?
A) 0.88
B) -0.88
C) 0
D) 1.40
A) 0.88
The scatter plot on page 108 displays the relationship between two random variables. What is the correlation coefficient of these two variables?
A) -0.98
B) 0.98
C) -0.98 and 0.98
D) 0
D) 0
The fitted regression equation for two vaiables x and y is y’ = -5x + 131. The coefficient of determination is 0.85, or 85%. What is the correlation coefficient?
A) -0.92
B) 0.92
C) 0.85
D) -1.45
A) -0.92
The correlation coefficient between the age of a car and its cost is r = -0.85. This means that:
A) changes in the age of the car cause the cost to change
B) as the age of a car increases, the cost of the car tends to increase.
C) as the age of a car increases, the cost of the car tends to decrease.
D) the cost of a car is controlled by its age.
C) as the age of a car increases, the cost of the car tends to decrease.
When the measurement for one sample tends to be dependent on teh measure for the previous sample, these data are called:
A) independent
B) autocorrelated
C) biased
D) inconsistent
B) autocorrelated
Which of the following can help identify special cause variation in a process?
A) Statistical process control
B) Regression
C) Histogram
D) Capability analysis
A) Statistical process control
A control chart was in control, but the operator adjusted the process anyway. What is this called?
A) Common cause variation
B) Special cause variation
C) Overcontrol
D) Undercontrol
C) Overcontrol
What is the principal purpose of control charts?
A) To identify the source of special cause variation in a process
B) To adjust a process when it goes out of control
C) To automate a process
D) To help process operators recognize the presence of special causes of variation
D) To help process operators recognize the presence of special causes of variation
Which of the following events would not be considered a source of common cause variation?
A) Measurement system variability
B) Incorrect machine settings
C) Variations in temperature
D) Slight changes in customer arrivals to a store
B) Incorrect machine settings
Which of the following statements about rational subgrouping is correct?
A) Variability within samples is minimized
B) Variability between samples is minimized
C) Variability within samples is maximized
D) There is no difference between within-sample variability and between-sample variability.
A) Variability within samples is minimized
Which quality leader introduced the use of control charts to monitor a quality characteristic?
A) Shewhart
B) Deming
C) Juran
D) Taguchi
A) Shewhart
What probability distribution is required to construct X(bar) and R control charts?
A) Binomial
B) Poisson
C) Normal
D) Uniform
C) Normal
An X(bar) and R chart was prepared for an operation using 25 samples with seven pieces in each sample. X(double bar) was found to be 24.8 and R(bar) was 5.50. During production, a sample of seven was taken and the pieces measured 25, 32, 35, 28, 27, 24, and 26. At the time this sample was taken:
A) both the average and range were within the control limits
B) neither the average nor range were within the control limits
C) only the average was outside the control limits
D) only the range was outside the control limits
B) neither the average nor range were within the control limits
The diameter of a steel rod is a quality characteristic of interest. Sample of size twelve will be selected in the subgroups. Which of the following control charts is preferred to monitor the process variability?
A) X(bar) and R chart
B) X(bar) and s chart
C) p-chart
D) c-chart
B) X(bar) and s chart
An X(bar) and s chart was prepared for an operation using 25 samples with six pieces in each sample. X(double bar) was found to be 12.68 and s(bar) was 2.45. During production, a sample of six was taken and the pieces measured 11, 13, 14, 14, 10, and 12. At the time this sample was taken:
A) Both the average and standard deviation were within the control limits
B) Neither the average nor standard deviation were within the control limits.
C) only the average was outside the control limits
D) only the standard deviation was outside the control limits.
A) Both the average and standard deviation were within the control limits
A company would like to monito a continuous quality characteristic of a product. However, it is expensive to obtain the measurements of this quality characteristic. Which of the following control charts is most appropriate to monitor this process?
A) I-MR chart
B) X(bar) and R chart
C) X(bar) and s chart
D) p-chart
A) I-MR chart
A hospital is monitoring the surgeries that result in surgical complications. The number of surgeries each month and those resulting in a complication were recorded. The number of surgeries each month can vary. Which of the following control charts is most appropriate to monitor this process?
A) X(bar) and R chart
B) p-chart
C) np-chart
D) c-chart
B) p-chart
A factory collected data on the number of nonconforming parts and constructed a p-chart. 15 samples of size 150 were collected. They determined that the average fraction of nonconforming parts was p(bar) = 0.037. During production, a sample of 150 parts was taken, of which 11 were nonconforming. At the time this sample was taken:
A) the sample was within the control limits
B) the sample was outside the control limits
C) the upper control limit was 0.073
D) the lower control limits was -0.01
A) the sample was within the control limits
What is the upper control limit for a p-chart when the average daily production is 3575 units with an established fraction defective of 0.048?
A) 0.0600
B) 0.7053
C) 0.0587
D) 0.6893
C) 0.0587
A team at a factory would like to monitor the number of defect in a TV screen. Twenty-five samples of five TB screens are inspected. Which of the following control charts is most appropriate for this scenario?
A) X(bar) and R chart
B) p-chart
C) np-chart
D) c-chart
D) c-chart
A team at a factory is monitoring the average number of defects in RB screens. Thirty five TV screens are randomly selected each day over a 25 day period. The average number of defects per TB screen was found to be u(bar) = 0.73. What is the upper control limit for a corresponding u-chart?
A) 1.24
B) 0.30
C) 1.16
D) 0.22
C) 1.16
A team would like to be able to detect small shifts in a process using a control chart. Which of the following control charts is most appropriate for this goal?
A) X(bar) and R chart
B) X(bar) and s chart
C) Individual chart
D) CUSUM chart
D) CUSUM chart
If a process is out of control, the probability that a single point on the X(bar chart will fall between plus two sigma and the upper control limit is:
A) 0.2240
B) 0.1587
C) 0.3413
D) Unknown
D) Unknown
If a process is in control, it is desirable to:
A) adjust the process when a point is not on target
B) have a small average run length
C) have a large average run length
D) stop monitoring the process
C) have a large average run length
Consider the MR chart (on page 113) of a normally distributed process. What conclusions can be drawn from this control chart?
A) The process is out of control
B) The process is stable
C) The process is operating within the specifications
D) The process is operating outside the specifications
A) The process is out of control
Consider the p-chart on page 114. What conclusions can be drawn from this control chart?
A) The process is out of control
B) The process is stable
C) The process is operating within the specifications
D) The process is operating outside the specifications
A) The process is out of control
Consider the X(bar) chart of a normally distributed process on page 114. What conclusions can be drawn from this control chart?
A) The process is out of control
B) The process is stable
C) The process is operating within the specifications
D) The process is operating outside the specifications
B) The process is stable
The main disadvantage of pre-control charts compared to a control chart is that:
A) the process is compared to a historic distribution in a pre-control chart
B) pre-control charts are not statistically based
C) Pre-control charts are harder to construct than control charts.
D) Pre-control charts are harder to interpret
B) pre-control charts are not statistically based
Which of the following is an advantage of pre-controlled charts?
A) Pre-control charts provide information on how a process can be brought
B) Pre-control charts provide information about how variability in a process can be reduced.
C) Pre-control charts can be used for processes whose capability ratio is less than one.
D) Pre-control charts are useful in setup operations to assess whether a product is produced between the tolerances.
D) Pre-control charts are useful in setup operations to assess whether a product is produced between the tolerances.
A manufacturing company received an order for a build-to-order product from a customer. The company would like to monitor the process; which of the following tools is most appropriate?
A) Pre-control chart
B) X(bar) and R control chart
C) Short-run SPC
D) Capability analysis
C) Short-run SPC
What is the first step in a capability study?
A) Compare the actual capability to the desired capability
B) Measure the process capability
C) Estimate the process parameters
D) Verify that the process is stable
D) Verify that the process is stable
A team would like to determine whether a process is able to meet customer specifications. What quality tool should they use?
A) Flowchart
B) Cause and effect diagram
C) Capability analysis
D) Regression analysis
C) Capability analysis
The dimension of a component has specifications 5.5 +/- 0.25. The process data are normally distributed with mean 5..45 and standard deviation 0.085. What fraction of components will have this dimension outside the specification limits?
A) 0.9904
B) 0.0096
C) 0.9998
D) 0.0002
B) 0.0096
The diameter of a stainless steel rod is an important quality characteristic. The rod has specifications 2.50 +/-0.05. Data from the process indicate the distribution is normally distributed, and an X(bar) and R chart indicates the process is stable. The control charts used a sample size of 7 and found that X(bar) = 2.5014 and R(bar) = 0.0568. What fraction of steel rods are within the specification limits?
A) 0.9825
B) 0.0175
C) 0.0071
D) 0.9896
A) 0.9825
Which of the following is the correct formula to find the specification limits of a quality characteristic?
A) μ ± 3σ
B) x(bar) ± (σ / √(n))
C) USL - LSL / 6σ
D) Specification limits are determined externally and do not have a generic formula
D) Specification limits are determined externally and do not have a generic formula
A stable, normally distributed process has specifications 21.35 ± 4.50. A sample of data from the process had a mean X(bar) = 20.98 and standard deviation σ = 1.10. Find Cp and Cpk.
A) Cp = 1.36, Cpk = 1.25
B) Cp = 1.25, Cpk = 1.36
C) Cp = 1.36, Cpk = 1.48
D) Cp = 2.73, Cpk = 1.36
A) Cp = 1.36, Cpk = 1.25
A stable process has specifications 14 ± 5. The process is normally distributed with mean 13 and standard deviation 1.5. Is this process considered capable?
A) Yes, since Cp = 1.11
B) Yes, since Cp = 0.89
C) No, since Cp = 0.89
D) No, since Cp = 1.33
C) No, since Cp = 0.89
The diameter of a stainless steel rod is an important quality characteristic. The rod has specification 2.50 ± 0.05. Data from the process indicate the distribution is normally distributed, and an X(bar and R chart indicates the process is stable. the control charts used a sample of size 7 and found that X(double bar) - 2.5014 and R(bar) = 0.0568. What is the capability of this process?
A) 0.79
B) 0.77
C) 0.82
D) 0.98
A) 0.79
Which of the following metrics is recommended to evaluated process capability when the process is not in statistical control?
A) Cp
B) Pp
C) Cpk
D) Cr
B) Pp
A textile company is designing an experiment to test the effects of a temperature, pressure, and time on tensile properties of a fiber composite. Each of these factors will be run at a high and low level. A full-factorial design is used with four replicates per run.
How many treatment combinations are in this experiment?
A) 3
B) 9
C) 8
D) 4
C) 8
A textile company is designing an experiment to test the effects of a temperature, pressure, and time on tensile properties of a fiber composite. Each of these factors will be run at a high and low level. A full-factorial design is used with four replicates per run.
How many factors are in this experiment?
A) 3
B) 4
C) 2
D) 12
A) 3
A textile company is designing an experiment to test the effects of a temperature, pressure, and time on tensile properties of a fiber composite. Each of these factors will be run at a high and low level. A full-factorial design is used with four replicates per run.
Variation observed in the readings of the replicates for each treatment combination is referred to as what?
A) Interaction
B) Experimental Error
C) Capability
D) Noise variable
B) Experimental Error
What is the first step in designing a successful experiment?
A) Choose the factors and responses
B) Select the experimental design
C) Define the method of measurement
D) State the objective of the experiment
D) State the objective of the experiment
What technique in experimental design will reduce the effect of uncontrolled variables that are not part of the experiment but might affect the response variable?
A) Confounding
B) Blocking
C) Randomization
D) Interaction
C) Randomization
An experiment is being conducted in a factory. Each experimental run takes several hours, so the experiment will last several days. What design technique would help in this experiment?
A) Confounding
B) Blocking
C) Randomization
D) Replication
B) Blocking
Which of the following statements on randomized block designs is not true?
A) The blocking factor is not modeled as an interaction with treatments
B) Determining whether the levels of the block factor are significant is not of interest
C) We do not need to include a blocking variable in the designed experiment
D) Including the blocking factor reduces its effect on the response
C) We do not need to include a blocking variable in the designed experiment
Consider the ANOVA table below for a one-factor experiment with a blocking variable. What conclusions can be drawn from this ANOVA table?
Var. Source dF SS MS F p-value
Factor A 4 198.0 49.5 12.05 0.004
Block 3 101.75 33.92
Error 12 79.25 6.60
Total 19 379.0
A) The blocking variable has a significant effect on the response
B) Factor A has a significant effect on the response
C) There is a significant interaction between factor A and the blocking variable
D) Both the blocking variable and factor A have a significant effect on the response.
B) Factor A has a significant effect on the response
True/False. Once an experiment has been carried our with blocking included, we can reanalyze the experiment as if it were not blocked.
A) True
B) False
B) False
An experiment is being conducted on the yield of a substance. Two factors are believed to have an effect on the yield. What type of design would be appropriate for his experiment?
A) Randomized block design
B) Interaction
C) Factorial design
D) Latin square
C) Factorial design
Consider the table on page 120 showing the results of a 2³ full factorial design. Assuming normality and equal variance assumptions are valid, which terms have a significant effect on the response variable?
A) A and B only
B) A, B, and AB
C) All main effects
D) C, AC, BC, and ABC
B) A, B, and AB
Which of the following graphical tools can help assess the assumption of independence when analyzing the results of a full-factorial design?
A) Contour plot
B) Normal probability plot
C) Histogram
D) Run chart
D) Run chart
A 2⁴ full factorial experiment is conducted with a single replicate. If all main effects and interactions are included in the model, how many degrees of freedom does the error term have?
A) 15
B) 1
C) 8
D) None
D) None
An experiment has eight factors at two levels each. The experiment has 128 runs. What is the experimental design called?
A) Full-factorial
B) Half-fractional factorial design
C) Taguchi design
D) None of the above
B) Half-fractional factorial design
An advantage of using a full-factorial design over a fractional factorial design is that:
A) all main effects and two-factor interactions are estimable
B) it has projection properties
C) it requires fewer runs
D) effects are confounded
A) all main effects and two-factor interactions are estimable
In a resolution IV fractional factorial experiment, main effects are confounded with:
A) three-factor and higher interactions
B) other main effects
C) two-factor and higher interactions
D) no other effects
A) three-factor and higher interactions
Consider an experiment with five factors each at two levels. Using the defining relation I = ABD = ACE = BCDE, with which effects is main effect B aliased?
A) BD and CE
B) BC< DE, ABE, and ACD
C) AD and CDE
D) B is not aliased with other effects.
C) AD and CDE
An experiment is being conducted to find the optimal ingredients for a cake mix. The experimenters want the taste of the cake to be unaffected by small variation in oven temperature in the customers homes. This is a problem of:
A) interaction
B) confounding
C) measurement error
D) robustness
D) robustness
A team conducted an experiment to determine to determine the optimal amount of three ingredients in a cake in order to maximize the taste. Two noise factors (oven temperature and backing time) were also included. A cress-array design was used. The analysis indicated that there was a significant interaction between one of the ingredients and the over temperature. Which of the following statements is true?
A) There is no robust design problem for this experiment
B) It may be possible to find settings of the ingredients that are robust to the oven temperature.
C) The oven temperature does not have an effect on the taste of the cake.
D) The three ingredients are uncontrollable factors in this experiment.
B) It may be possible to find settings of the ingredients that are robust to the oven temperature.
