Deck 12: Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

Question 1

Examine the given run chart or control chart and determine whether the process is within_
statistical control. If it is not, identify which of the three out-of-statistical-control criteria apply.

Answer 1

The process appears to be out of statistical control. There is a cyclical pattern.

Question 2

Are control charts based on actual behavior or on desired behavior? Give an example to
illustrate the difference between the two types of behavior.

Answer 2

Control charts are based on actual behavior. The control limits are based on the actual behavior of the process. They
are not related to the desired specifications indicated by the manufacturer. For example, it is possible to
manufacture rulers that are in statistical control but are consistently 14 inches long, indicating that the desired
behavior is not occurring.

Question 3

Construct an R chart and determine whether the process variation is within statistical control.
Control Chart Constants

Answer 3

The process appears to be within statistical control.

Question 4

Sketch a control chart that indicates that a process is not statistically stable due to the run of 8
rule.

Question 5

Question 6

Construct an R chart and determine whether the process variation is within statistical control.
Control Chart Constants

Question 7

Describe the three criteria used to determine if a control chart indicates a process which is not_
statistically stable.

Question 8

Describe a run chart and give an example. Refer to the values on each of the axes as you
describe the run chart.

Question 9

A control chart for R is shown below. Determine whether the process variation is within_
statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection
of statistically stable variation.

Question 10

Question 11

Examine the given run chart or control chart and determine whether the process is within_
statistical control. If it is not, identify which of the three out-of-statistical-control criteria apply.

Question 12

Provide an appropriate response. Describe what process data are. Why are process data
important to businesses? What is a common goal of businesses using quality control?

Question 13

A control chart for is shown below. Determine whether the process mean is within_
statistical control. If it is not, identify which of the three out-of-control criteria lead to
rejection of a statistically stable mean.

Question 14

Define statistically stable (or "within statistical control"). Show examples of run charts which
illustrate processes which are not statistically controlled. Discuss the pattern which indicates
the process is not statistically controlled for each example.

Question 15

Use the given process data to construct a control chart for p. A manufacturer monitors the level_
of defects in the television sets that it produces. Each week, 200 television sets are randomly
selected and tested and the number of defects is recorded. The results for 12 consecutive weeks
are shown below.

Question 16

Construct a run chart for individual values corresponding to the given data. A machine is
supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is
tested; the results are given below.

Question 17

Examine the given run chart or control chart and determine whether the process is within
statistical control. If it is not, identity which of the three out-of-statistical-control criteria
apply. A run chart for individual values W is shown below. Does there appear to be a pattern
suggesting that the process is not within statistical control? If so, describe the pattern.

Question 18

A common goal of quality control is to reduce variation in a product or service. List and_
describe the two types of variability. Give an example of each.

Question 19

Describe an R chart and give an example. What does it attempt to monitor?

Question 20

Use the given process data to construct a control chart for p. If the weight of cereal in a_
particular packet is less than 14 ounces, the packet is considered nonconforming. Each week,
the manufacturer randomly selects 1,000 cereal packets and determines the number that are
nonconforming. The results for 12 consecutive weeks are shown below.

Question 21

Construct an R chart and determine whether the process variation is within statistical control._

Question 22

Examine the given run chart or control chart and determine whether the process is within_
statistical control. If it is not, identify which of the three out-of-statistical-control criteria apply.

Question 23

Use the given process data to construct a control chart for p. A manufacturer monitors the level_
of defects in the television sets that it produces. Each week, 200 television sets are randomly
selected and tested and the number of defects is recorded. The results for 12 consecutive weeks
are shown below.

Question 24

Describe the three criteria used to determine if a control chart indicates a process which is not_
statistically stable.

Question 25

Examine the given run chart or control chart and determine whether the process is within
statistical control. If it is not, identify which of the three out-of-statistical-control criteria
apply.

Question 26

Use the given process data to construct a control chart for p. A drugstore considers a wait of
more than 5 minutes to be a defect. Each week 100 customers are randomly selected and
timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below.

Question 27

Construct an chart and determine whether the process variation is within statistical control.

A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes.

Question 28

A control chart for attributes is to be constructed.
limits, a process which has been having a 5% rate of nonconforming items, or a process which
has been having a 10% of nonconforming items? Assume that both processes have the same
sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a
shift from 10% to 15%? Explain your reasoning.

Question 29

A control chart for R is shown below. Determine whether the process variation is within_
statistical control. If it is not, identify which of the three out-of-control criteria lead to
rejection of statistically stable variation.

Question 30

A control chart for is shown below._
statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection
of a statistically stable mean.

Question 31

Sketch a run chart that that indicates that a process is not statistically stable due to increasing
variation.

Question 32

Construct a run chart for individual values corresponding to the given data. A machine that is_
supposed to produce ball bearings with a diameter of 7 millimeters yields the following data
from a test of 5 ball bearings every 20 minutes.

Question 33

Provide an appropriate response. A common goal of quality control is to reduce variation in a
product or service. List and describe the two types of variability. Give an example of each.

Question 34

Question 35

Describe a p chart and give an example.

Question 36

A run chart for individual values is shown below. Does there appear to be a pattern suggesting
that the process is not within statistical control? If so, describe the pattern.

Question 37

Define statistically stable (or "within statistical control"). Show examples of run charts which
illustrate processes which are not statistically controlled. Discuss the pattern which indicates
the process is not statistically controlled for each example.

Question 38

A control chart for is shown below._
statistical control. If it is not, identify which of the three out-of-control criteria lead to
rejection of a statistically stable mean.

Question 39

Examine the given run chart or control chart and determine whether the process is
within statistical control. If it is not, identify which of the three out-of-statistical-control
criteria apply.

Question 40

Consider process data consisting of the amounts of potato chips (in ounces)in randomly selected bags of chips. The process is to be monitored with control charts based on samples
Of 50 bags randomly selected each day for 15 consecutive days of production. What does
X
Denote?

A)The mean of 50 bags.
B)The mean of all 15 sample means.
C)The mean of the ranges for the 15 days.
D)The mean of the standard deviations for the 15 days.

Question 41

__________________ variation results from causes that can be identified._

A)Random
B)Identifiable
C)Assignable
D)Definable

Question 42

Use the given process data to construct a control chart for p. A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and
Timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. What is the value of the upper control limit?

A)1
B)0.0783
C)0.0622
D)6.2

Question 43

________________ measurement of a characteristic or good or services that result from some combination of
Equipment, people, materials, methods, and conditions.

A)Process
B)Service
C)Sequential
D)Material

Question 44

R charts are used to monitor_____________._

A)means
B)proportions
C)variation
D)correlation

Question 45

List the advantages and disadvantages of nonparametric tests._

Question 46

Which graph using individual data values instead of a process characteristic?

Question 47

Examine the given run chart or control chart and determine whether the process is within_ statistical control.

A)The process is within statistical control.
B)The process is not within statistical control.

Question 48

Control charts are used to monitor changing characteristics of data over ____________._

A)time
B)space
C)distance
D)speed

Question 49

Examine the given run chart or control chart and determine whether the process is within statistical control.

A)The process is within statistical control.
B)The process is not within statistical control.

Question 50

Examine the given run chart or control chart and determine whether the process is within_ statistical control.

A)The process is within statistical control.
B)The process is not within statistical control.

Question 51

Examine the given run chart or control chart and determine whether the process is within statistical control.

A)The process is within statistical control.
B)The process is not within statistical control.

Question 52

Which type of chart would be best for monitoring the proportion of items that are defective?

Question 53

The centerline for a control chart for R consists of _______________._

A)the mean of the sample ranges
B)the mean of the sample data
C)the median
D)the standard deviation

Question 54

Use the given process data to construct a control chart for p. A candy manufacturer considers a cracked piece of candy to be a defect. Each day 100 candies are randomly selected and
Checked for cracks. The numbers of defects for 20 consecutive days are given below. What is the value of the center line?

A)6.6
B)10
C)0.066
D)1.32

Question 55

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean and range (in hours)of the lifetimes of the 10 lightbulbs are calculated. The results for
12 consecutive days are shown in the table below. Construct an R chart to determine whether
The process is in statistical control.
$\begin{array}{c|c|c|c}\text { Day } & \bar{x} & \text { Range } & s \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3 \\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\end{array}$

$\text { Control Chart Constants }$

$\begin{array}{lllllll}&\bar{x}&&s&&R\\\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777\end{array}$

A) $\text { The process is within statistical control. }$
B) $\text { The process is not within statistical control. }$

Question 56

A _________________ is a sequential plot of individual data values over time. One axis is used_ for the data values, and the other axis is used for the time sequence.

A)run chart
B)process chart
C)time-process chart
D)flow chart

Question 57

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour. What would be the centerline for a control chart for $\bar{x} ?$
$\begin{array}{c|cccc|c|l}\text { Sample } &&&{\text { bottle Volume (oz) }} && \overline{\boldsymbol{x}} & \text { Range } \\\hline1 & 19.9 & 20.1 & 20.2 & 20.3 & 20.125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.250 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.350 & 0.7 \\4 & 20.4 & 20.1 & 20.1 & 19.9 & 20.125 & 0.5 \\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.700 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7 & 19.525 & 0.3 \\7 & 19.8 & 19.4 & 19.6 & 19.7 & 19.625 & 0.4 \\8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925 & 0.2 \\9 & 20.2 & 20.3 & 20.1 & 20.3 & 20.225 & 0.2 \\10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125 & 0.3 \\11 & 20.3 & 20.5 & 20.1 & 20.2 & 20.275 & 0.4 \\12 & 20.1 & 19.9 & 19.8 & 19.7 & 19.875 & 0.4 \\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.650 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.400 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.650 & 0.4\end{array}$

A) $0.380 \text { milliliters }$
B) $19.935\text { milliliters }$
C) $20.000\text { milliliters }$
D) $20.212 \text { milliliters }$

Question 58

Use the Wilcoxon signed -ranks test to test the claim that the matched pairs have differences_
that come from a population with a median equal to zero. Eleven runners are timed at the 100-
meter dash and are timed again one month later after following a new training program. The
times (in seconds)are shown in the table. Use Wilcoxon's signed-ranks test and a significance
level of 0.05 to test the claim that the training has no effect on the times.

Question 59

Which of the following is not one of the criteria for determining if a control chart indicates that_ a process is not statistically stable?

A)Exceptional value
B)Upward shift
C)Downward trend
D)Decreasing variation

Question 60

Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4,_
5, 5, 5, 7, 8, 12, 12, 15, 18).

Question 61

Describe the sign test. What types of hypotheses is it used to test? What is the underlying
concept?

Question 62

Use the runs test to determine whether the given sequence is random. Use a significance level_
of 0.05. A true-false test had the following answer sequence. Test the null hypothesis that the sequence was random.

Question 63

Provide the appropriate response. Describe the Wilcoxon signed-ranks test. What types of_
hypotheses is it used to test? What assumptions are made for this test?

Question 64

A standard aptitude test is given to several randomly selected programmers, and the scores are
given below for the mathematics and verbal portions of the test. Use the sign test to test the
claim that programmers do better on the mathematics portion of the test. Use a 0.05 level of
significance.

Question 65

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal_
medians. Listed below are grade averages for randomly selected students with three different
categories of high-school background. At the 0.05 level of significance, test the claim that the
three groups have the same median grade average.

Question 66

Use the rank correlation coefficient to test for a correlation between the two variables. A_
placement test is required for students desiring to take a finite mathematics course at a
university. The instructor of the course studies the relationship between students' placement
test score and final course score. A random sample of eight students yields the following data. Compute the rank correlation coefficient, rs, of the data and test the claim of correlation
between placement score and final course score. Use a significance level of 0.05.

Question 67

Use the sign test to test the indicated claim. Fourteen people rated two brands of soda on a scale_
of 1 to 5. At the 5 percent level, test the null hypothesis that the two brands of soda are equally popular.

Question 68

Use the rank correlation coefficient to test for a correlation between the two variables.
Given that the rank correlation coefficient, rs, for 37 pairs of data is 0.324, test the claim of
correlation between the two variables. Use a significance level of 0.01.

Question 69

Use a 0.05 level of significance to test the claim that the sequence of computer -generated
numbers is random. Test for randomness above and below the mean.

Question 70

Use the runs test to determine whether the given sequence is random. Use a significance level_
of 0.05. The sequence of numbers below represents the maximum temperature (in degrees
Fahrenheit)in July in one U.S. town for 30 consecutive years. Test the sequence for
randomness above and below the median.

Question 71

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from
populations with equal medians. Use the Wilcoxon rank-sum approach to test the claim that
the sample student grade averages at two colleges come from populations with the same
median. The sample data is listed below. Use a 0.05 level of significance, and assume that the
samples were randomly selected.

Question 72

When applying the runs test for randomness above and below the median for 12 dollar/Euro
exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

Question 73

Describe the Wilcoxon rank-sum test. What type of hypotheses is it used to test? What
assumptions are made for this test? What is the underlying concept?

Question 74

Explain what an efficiency rating is. You may use an example to explain this concept. Do
comparable parametric or nonparametric tests have higher efficiency ratings?

Question 75

Solve the problem. Critical values for the runs test for randomness can be calculated by listing_
all possible sequences. Using the elements B, B, B, R, R, R list the 20 different possible
sequences. Find the number of runs for each sequence. Are you able to find 5% cutoff values
for G? What do you conclude?

Question 76

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from_
populations with equal medians. SAT scores for students selected randomly from two different
schools are shown below. Use a significance level of 0.05 to test the claim that the scores for
the two schools are from populations with the same median.

Question 77

Describe the rank correlation test. What types of hypotheses is it used to test? How does the
rank correlation coefficient rs differ from the Pearson correlation coefficient r?

Question 78

Use the sign test to test the indicated claim. The heights of 16 randomly selected women are
given below. Use a significance level of 0.05 to test the claim that the population median is
equal to 64.0 inches.

Question 79

Give at least two examples of nonparametric tests and their comparable parametric tests.

Question 80

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal_
medians. Listed below are grade averages for randomly selected students with three different
categories of high-school background. At the 0.05 level of significance, test the claim that the
three groups have the same median grade average.