FINAL #1

Question 1

a graphical tool used to find the association between two variables.

Answer 1

SCATTERPLOT

Question 2

A 2-sample t-test is applicable when:

a.
None of the above

b.
We want to compare the mean of one sample group with a standard.

c.
We want to compare the medians of two sample groups.

d.
We want to compare the mean of two independent sample groups with each other.

Answer 2

We want to compare the mean of two independent sample groups with each other.

Question 3

T/F
A Pareto chart is based on the 80/20 rule stating that 80% of defects are caused by 20% of the reasons. It plots the data in descending order, starting from the highest and going to the lowest.

Answer 3

TRUE

Question 4

A Belt has applied Box-Cox transformation on the y data. What should she to do next?

a.
Check the normality of the data to confirm.

b.
Perform residual analysis.

c.
Apply nonparametric tests on the transformed data.

d.
Proceed with the transformed data. There is no need to check data normality, as Box-Cox transformation always converts data to normal.

Answer 4

B. Box-Cox transformation is used to convert non-normal data into normal data. In Box-Cox transformation, each value of y is raised to the power of λ, where λ ranges between -5 and 5. It is recommended to confirm normality on transformed data after applying Box-Cox because even though Box-Cox transformation often converts non-normal data to normal, it is not always guaranteed

Question 5

A fast food restaurant has implemented a new visual system to ensure that the right amount of hamburgers are cooked to meet customer demand. What type of Lean tool was implemented?

a.
Kaizen

b.
5S

c.
Kanban

d.
Standard work

Answer 5

C. Kanban is a visual signal used to ensure that the right amount of product is produced or stocked to meet customer demand.

Question 6

T/F
Fourteen consecutive points alternating up and down is one of the eight rules of SPC in a control chart for variable data type, which indicates the process has a non-random pattern linked to some special causes.

Answer 6

TRUE

Question 7

A quality manager divides the total population into smaller similar groups for sampling. Then he randomly selects samples proportionally. Which type of sampling is this?

a.
Cluster sampling

b.
Group sampling

c.
Stratified random sampling

d.
Random sampling

Answer 7

B. When a population is broken into groups or strata and then random sampling is performed, it is called stratified random sampling.

Question 8

An invoice contains five fields. Fifty forms were sampled and 15 defects were found. What is the DPMO for the scenario?

a.
0.06

b.
60000

c.
6666

d.
None of the above

Answer 8

DPMO = (No. of defects × 1,000,000)/(No. of units × opportunities) = (15 × 1,000,000)/(50 × 5) = 60,000.

The correct answer is: 60000

Question 9

T/F
Appraisal cost and prevention cost are not examples of cost of poor quality, or COPQ.

a.
False

b.
True

Answer 9

Cost of quality (COQ) can be classified as COGQ (cost of good quality) and COPQ (cost of poor quality). COGQ includes prevention and appraisal costs, while COPQ consists of internal and external failure costs.

FALSE

Question 10

T/F
The empirical rule can be broken down into three parts: 68% of data fall within the first standard deviation from the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

Answer 10

TRUE

Question 11

Consider a manufacturing facility that produces 250 units of product per 5-day week. The facility is operating for one 8-hour shift each working day. What is the average throughput rate and the cycle time for the facility?

a.
6.25 units/h.; 9.6 minutes

b.
5.75 units/hr; 10.4 minutes

c.
6.25 units/hr; 10.4 minutes

d.
5.75 units/hr; 9.6 minutes

Answer 11

A. Throughput = units produced/time taken. Throughput = 250 units/5 days = 250 units/5 x 8 hr = 6.25 units/hr. Cycle time = 1/throughput. Cycle time = (1/6.25) hr = (60/6.25) min = 9.6 minutes.

The correct answer is: 6.25 units/h.; 9.6 minutes

Question 12

Consider the below figure of Processes A, B, and C in a production line from a manufacturing unit. One hundred parts enter Process A, and 120 parts are received as an output from Process C. For Processes A, B, and C, 19, 26, and 5 parts are rejected, respectively. Just before Process B and Process C, some parts are added from the intermediate parts inventory. What is the RTY for the production line?

Answer 12

Refer to the calculations in the figure below: Rolled throughput yield (RTY) for entire production line = (First Pass Yield of Process A) x (First Pass Yield of Process B) x (First Pass Yield of Process C) = (81%) x (75%) x (96%) = 0.81 x 0.75 x 0.96 = 0.5832, or 58%.

The correct answer is: 58%

Question 13

CUSUM charts are effective in detecting small shifts, while Shewhart charts are not effective in detecting such small process shifts.

a.
True

b.
False

Answer 13

true
CUSUM charts are effective In detecting small shifts, that is less than 1, whereas Shewhart charts are effective in detecting comparatively larger process shifts.

Question 14

During a 1-sample t-test, the output has a p-value of 0.06. At 95% confidence, a Belt should reject the null hypothesis.

a.
True

b.
False

Answer 14

Correct answer: B. There are two types of hypotheses in Six Sigma: null hypothesis and alternative hypothesis. A null hypothesis is rejected when the p-value is less than 0.05. Similarly, if the p-value is greater than 0.05, the null hypothesis cannot be rejected.

Question 15

During a Six Sigma project, a Belt has established a linear regression line with an equation of the form Y = 241 − 20.8X, where X is the independent variable and Y is the dependent variable. The value of 241 in the equation is called the ________ and the value “-20.8” in the given equation is the ________.

a.
slope; intercept

b.
Y-intercept; slope

c.
X-intercept; slope coefficient

d.
slope; slope coefficient

Answer 15

A. In a simple linear regression model, we get output as an equation of line with the slope and the Y-intercept of the line. In the equation Y = a + bx, b is the slope and a is the Y-intercept.

Question 16

Failing to reject a false null hypothesis is called a type 2 error.

a.
True

b.
False

Answer 16

: A. The second type of error that can be made in significance testing is failing to reject a false null hypothesis. This kind of error is called a type 2 error. If the null hypothesis is false, then the probability of a type 2 error is called β (beta).

Question 17

the data shown below, a Belt suspects the three teams are performing equally in terms of TAT (turnaround time). Which hypothesis test should he perform to see if all are equal considering the data is non-normal?
a.
Mood’s median

b.
3-sample t-test

c.
ANOVA

d.
Mean

Answer 17

A. Mood’s median test

1 categorial factor and a continuous response

Question 18

if one of the tails of the distribution is longer than the other, it is called:

a.
Skewed distribution.

b.
Kurtosis.

c.
Normal distribution.

d.
None of the above.

Answer 18

Correct answer: A. Skewness is a term in statistics used to describe asymmetry from the normal distribution in a set of statistical data. Skewness can come in the form of negative skewness or positive skewness, depending on whether data points are skewed to the left and negative or to the right and positive of the data average.

Question 19

If the process mean is not at the target, then we should calculate Cp instead of Cpk to determine process capability.

a.
True

b.
False

Answer 19

B. Cpk addresses the process cantering issues. If the process mean is not at the center or target, then Cpk is different from Cp, and it shows the correct capability of the process. If the process mean coincides with the target, then Cp and Cpk both are the same.

cp- ability of a process to justify the structure specification for a product. Cpk portrays deviation of a process from the center within the tolerance range.

Question 20

In a hypothesis test for means, a sample size of 30 calls has produced a mean of 8 minutes with a standard deviation of 2 minutes per call−hold time. The customer specification for AHT (average hold time) is 8 minutes. At a 5% significance level, what should the customer do?

a.
State that the population mean is greater than 8 minutes.

b.
Accept the call’s hold time.

c.
Reject the call’s hold time.

d.
Change its specification to 8 minutes.

Answer 20

C. C.I. = mean ± Z0.5/2 × Std. dev./Sqrt(sample size) = 8 ± 1.96 × 2/sqrt(30) = (7.284, 8.716). The target or customer’s specification of 8 minutes is inside the 95% confidence interval (CI) is (7.284, 8.716), so there is no significant difference between the call process’s hold time mean and the customer’s AHT.

Question 21

Refer to the following run chart and comment on the stability of the process (assume a 90% confidence level).
Run Chart

a. Clustering is prominent at 90% confidence.

b.
Mixtures are prominent at 90% confidence.

c.
Clustering and trends observed as p-values are high.

d.
Mixtures and oscillations observed as p-values are low.

Answer 21

B A run chart is used to monitor the process stability over time, and it produces the four components that explain stability: cluster, trends, mixtures, and oscillation. P-values are obtained for each of the four components. If the p-value is less than 10%, then that component is supposed to be impacting process stability at 90% confidence. The p-value of mixtures is 0.084, which is less than 0.10, so mixtures are prominent at 90% confidence

Question 22

The documentation and administration cost for a project is $6,500, and the project required an initial investment of $47,500. If the project yields monthly savings of $3,500 after 4 months, what is the payback period in months?

a.
15.4

b.
23.7

c.
19.4

d.
9.7

Answer 22

Total Cost = $54,000 (6,500 + 47,500). Payback Period = $54,000/$3,500 = 15.4 months. Because the savings begin after 4 months, the total payback period = 15.4 + 4 months = 19.4 months.

Question 23

true/false

The Mann-Whitney Test is a nonparametric alternative test to the independent 2-sample t-test

Answer 23

true

Question 24

The process capability, Cpk, reported for a process with an average of 60 units, a spread of 6 units, and upper and lower specification limits of 85 and 65 units, respectively, would be:

a.
6.67

b.
3.33

c.
8.33

d.
1.67

Answer 24

The mean value 60 is close to LSL 65 in comparison to USL of 85. Spread = 6 = 6 times Std. dev. Hence Cpk = Cpl = (Mean − LSL)/3 times Std. dev. Cpk = (65 − 60)/3 = 5/3 = 1.67.

Question 25

What type of control chart should be used when the data are continuous, in time order, and have a subgroup size of 7?

a.
Individuals

b.
X-bar R

c.
X-bar S

d.
NP

Answer 25

x-bar R (2-10)

Question 26

What would be the reported Ppk for a new process with an average of 94 units, a spread of 22 units based on collected sample data, and upper and lower specification limits of 125 and 80 units, respectively?

a.
2.81

b.
1.27

c.
0.64

d.
2.05

Answer 26

B. Sample mean is close to LSL = 80. Sample spread = 22 = 6 times sample std. Dev., so 3 times sample std. dev.= 22/2 = 11. Ppk = (Sample Mean − LSL)/3 times Sample Std. Dev. Ppk = (94 − 80)/11 = 14/11 = 1.273.

Question 27

Which hypothesis test would you use when you want to compare median scores of two dependent samples of a dependent variable that is not normally distributed?

a.
2-sample t-test

b.
Mood’s median test

c.
Wilcoxon sign test

d.
Chi-square test

Answer 27

he Wilcoxon signed-rank test or Wilcoxon sign test is a nonparametric analysis that statistically compares the medians of two dependent samples and assesses for significant differences. The Wilcoxon sign test is the nonparametric alternative of the dependent samples t-test or paired-t test.

Question 28

Which is not a part of the measure of central tendency?

a.
Mean

b.
Mode

c.
Range

d.
Median

Answer 28

Range is the difference between the highest and lowest value in a data set. It is a measure of dispersion. The others (mean, median, and mode) are measures of central tendency.

Question 29

Which of the following ways can be used to check the normality of a data set?

a.
Box plot

b.
Probability plot

c.
Anderson-Darling test

d.
Anderson-Darling test and probability plot

e.
Anderson-Darling test, probability plot, and box plot

Answer 29

The Anderson-Darling test and probability plot are used to assess the normality of data. The box plot is primarily used to compare the distributions of data pertaining to categorical variables (e.g., comparing the AHT data of two shifts from a call center to identify the presence of outliers).

Question 30

Which test is used to compare means of more than two sample groups for normal data?

a.
T-test

b.
ANOVA

c.
Mood’s median

d.
F-test

Answer 30

ANOVA stands for analysis of variance. This hypothesis test is used to compare means of more than two samples. Two prerequisites of ANOVA are that data should follow a normal distribution and the variance of the samples should be equal.

Question 31

Which underlying distribution is assumed while performing a 2-proportions hypothesis test?

a.
Chi-square

b.
t

c.
Poisson

d.
Binomial

Answer 31

A 2-proportions test assumes an underlying binomial distribution