Business Statistics and Operations Management Questions and Answers

Q: The R chart monitors :

The R chart monitors changes in the dispersion or variability of a process.The R (range) chart plots the range of each sample, the difference between its largest and smallest values, to detect whether the variability of the process has changed. It is used with the X-bar chart, which monitors the process average.The proportion of defects is monitored by the p chart, the actual number of defects by the c chart, and the subgroup average by the X-bar chart.

Q: The mode has all of the following disadvantages except :

The exception is the mode is unduly affected by extreme values; that is not a disadvantage of the mode.The mode is the most frequent value, so a few very large or very small values do not change it. That insensitivity to extreme values is in fact an advantage of the mode; it is the mean that is unduly affected by extreme values.The other three are genuine disadvantages: a data set may have no mode (all values occur once), every value may be a mode, and a data set with several modes is hard to interpret.

Q: Open ended questions produce :

Open-ended questions produce Qualitative data.An open-ended question lets respondents answer in their own words, for example 'What do you like about this product?' The answers are descriptive text: opinions, reasons and experiences that give depth but must be interpreted or coded before they can be counted.Closed-ended questions with fixed choices produce quantitative data that can be counted directly. Open-ended questions certainly produce data, and their data are not 'easy': they are harder to analyse than closed answers.

Q: When the population is divided into subsets such that the units within the subset are as homogeneous as possible and are heterogeneous among themselves, the sampling method is called as.................

This is Stratified sampling.In stratified sampling the population is divided into strata such that units within each stratum are as alike as possible, while the strata differ from one another. A sample is then drawn from every stratum, which makes the sample more representative and the estimates more precise.Cluster sampling is the reverse: each cluster should be as varied as the population, and whole clusters are sampled. Quota sampling is non-random selection to fill quotas, and systematic sampling selects every k-th unit from a list.

Q: The main difference between Z and t-tests is :

The difference is that for the Z-test the population mean and standard deviation are needed.The Z-test assumes the population standard deviation is known (or the sample is large enough to treat the sample estimate as known), and uses the normal distribution. When the population standard deviation is unknown and must be estimated from a small sample, the t-test is used, with the t distribution and n − 1 degrees of freedom.The first option reverses the two tests. The t-test needs the sample standard deviation as well as the mean, not the mean only. And the tests are not identical apart from sample size; they use different distributions.

Q: The covariance of two random variables :

The covariance of two random variables does not have an upper or lower bound.Covariance is the average product of the deviations of two variables from their means. Its size depends on the units and scale of the variables, so it can be any positive or negative number. This is why the correlation coefficient, which divides covariance by the two standard deviations, is used to get a bounded measure between −1 and +1.The other statements are false: the sign of the covariance does show the direction of the relationship, it can be negative, and its unit is the product of the two variables' units.

Q: The critical path of a project network diagram has :

The critical path has the longest duration.In a project network the critical path is the longest path, in time, from start to finish. Its length is the shortest possible completion time of the project, and its activities have zero slack, so any delay in them delays the whole project.The shortest path would leave longer paths unfinished. The number of nodes on a path, odd or even, has nothing to do with whether it is critical.

Q: The chart used to monitor the number of non-conforming units of a process is :

The number of non-conforming units is monitored with the np chart.The np chart is an attribute control chart that plots the number of defective (non-conforming) units in samples of constant size n. Its counterpart, the p chart, plots the proportion defective and allows the sample size to vary.The c chart counts defects (non-conformities) per unit or area, where one unit may have several defects. The X chart and R chart are variable charts for the process mean and range of measurements, not counts of defective units.

Q: Which one of the following is not a type of supply chain design ?

Economic logistics is not a type of supply chain design.Cross docking moves incoming goods directly onto outbound vehicles with little or no storage. Reverse distribution handles the flow of goods back from customers, for returns, repair or recycling. Third-party logistics outsources logistics functions to a specialist provider. Each is a recognised way of designing the supply chain.'Economic logistics' is not a recognised supply chain design, so it is the odd one out.

Q: Which of the following is not a true statement about the Binomial Probability Distribution ?

The statement that is not true is The random variable of interest is continuous.The binomial random variable counts the number of successes in \(n\) trials, so it can take only the whole numbers 0, 1, 2 and so on up to \(n\). It is a discrete distribution:\[ P(X = x) = \binom{n}{x} p^{x} (1 - p)^{n - x} \]The other three statements are the conditions of a binomial experiment: a fixed number of independent trials, each with only two outcomes (success or failure), and the same probability of success \(p\) on every trial.

21.

The R chart monitors :

A.Proportion of defects
B.Changes in the dispersion or variability
C.Actual number of defects
D.Subgroup average

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

The R chart monitors changes in the dispersion or variability of a process.

The R (range) chart plots the range of each sample, the difference between its largest and smallest values, to detect whether the variability of the process has changed. It is used with the X-bar chart, which monitors the process average.

The proportion of defects is monitored by the p chart, the actual number of defects by the c chart, and the subgroup average by the X-bar chart.

Discuss in Forum

22.

The mode has all of the following disadvantages except :

A.A data set may have no modal value
B.Every value in a data set may be a mode
C.A multimodal data set is difficult to analyze
D.The mode is unduly affected by extreme values

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: D

The exception is the mode is unduly affected by extreme values; that is not a disadvantage of the mode.

The mode is the most frequent value, so a few very large or very small values do not change it. That insensitivity to extreme values is in fact an advantage of the mode; it is the mean that is unduly affected by extreme values.

The other three are genuine disadvantages: a data set may have no mode (all values occur once), every value may be a mode, and a data set with several modes is hard to interpret.

Discuss in Forum

23.

Open ended questions produce :

A.Quantitative data only
B.Qualitative data
C.No data
D.Easy data

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

Open-ended questions produce Qualitative data.

An open-ended question lets respondents answer in their own words, for example 'What do you like about this product?' The answers are descriptive text: opinions, reasons and experiences that give depth but must be interpreted or coded before they can be counted.

Closed-ended questions with fixed choices produce quantitative data that can be counted directly. Open-ended questions certainly produce data, and their data are not 'easy': they are harder to analyse than closed answers.

Discuss in Forum

24.

When the population is divided into subsets such that the units within the subset are as homogeneous as possible and are heterogeneous among themselves, the sampling method is called as.................

A.Quota sampling
B.Systematic sampling
C.Stratified sampling
D.Cluster sampling

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: C

This is Stratified sampling.

In stratified sampling the population is divided into strata such that units within each stratum are as alike as possible, while the strata differ from one another. A sample is then drawn from every stratum, which makes the sample more representative and the estimates more precise.

Cluster sampling is the reverse: each cluster should be as varied as the population, and whole clusters are sampled. Quota sampling is non-random selection to fill quotas, and systematic sampling selects every k-th unit from a list.

Discuss in Forum

25.

The main difference between Z and t-tests is :

A.For t-test, the population mean and standard deviation are needed
B.For Z-test the population mean and standard deviation are needed
C.For t-test only sample mean is needed
D.The t-test and Z-test are identical except of sample size used

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

The difference is that for the Z-test the population mean and standard deviation are needed.

The Z-test assumes the population standard deviation is known (or the sample is large enough to treat the sample estimate as known), and uses the normal distribution. When the population standard deviation is unknown and must be estimated from a small sample, the t-test is used, with the t distribution and n − 1 degrees of freedom.

The first option reverses the two tests. The t-test needs the sample standard deviation as well as the mean, not the mean only. And the tests are not identical apart from sample size; they use different distributions.

Discuss in Forum

26.

The covariance of two random variables :

A.Does not have an upper or lower bound
B.Does not provide an indication of the direction of the relationship between the variables
C.Is a positive number
D.Has no measurement unit

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: A

The covariance of two random variables does not have an upper or lower bound.

Covariance is the average product of the deviations of two variables from their means. Its size depends on the units and scale of the variables, so it can be any positive or negative number. This is why the correlation coefficient, which divides covariance by the two standard deviations, is used to get a bounded measure between −1 and +1.

The other statements are false: the sign of the covariance does show the direction of the relationship, it can be negative, and its unit is the product of the two variables' units.

Discuss in Forum

27.

The critical path of a project network diagram has :

A.Shortest duration
B.Odd number of nodes
C.Longest duration
D.Even number of nodes

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: C

The critical path has the longest duration.

In a project network the critical path is the longest path, in time, from start to finish. Its length is the shortest possible completion time of the project, and its activities have zero slack, so any delay in them delays the whole project.

The shortest path would leave longer paths unfinished. The number of nodes on a path, odd or even, has nothing to do with whether it is critical.

Discuss in Forum

28.

The chart used to monitor the number of non-conforming units of a process is :

A.C chart
B.X chart
C.R chart
D.np chart

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: D

The number of non-conforming units is monitored with the np chart.

The np chart is an attribute control chart that plots the number of defective (non-conforming) units in samples of constant size n. Its counterpart, the p chart, plots the proportion defective and allows the sample size to vary.

The c chart counts defects (non-conformities) per unit or area, where one unit may have several defects. The X chart and R chart are variable charts for the process mean and range of measurements, not counts of defective units.

Discuss in Forum

29.

Which one of the following is not a type of supply chain design ?

A.Cross Docking
B.Reverse distribution
C.Third party logistics
D.Economic logistics

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: D

Economic logistics is not a type of supply chain design.

Cross docking moves incoming goods directly onto outbound vehicles with little or no storage. Reverse distribution handles the flow of goods back from customers, for returns, repair or recycling. Third-party logistics outsources logistics functions to a specialist provider. Each is a recognised way of designing the supply chain.

'Economic logistics' is not a recognised supply chain design, so it is the odd one out.

Discuss in Forum

30.

Which of the following is not a true statement about the Binomial Probability Distribution ?

A.Each trial is independent
B.Outcome of each trial can be classified as either a success or a failure
C.The random variable of interest is continuous
D.The probability of success must be constant from trial to trial

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: C

The statement that is not true is The random variable of interest is continuous.

The binomial random variable counts the number of successes in \(n\) trials, so it can take only the whole numbers 0, 1, 2 and so on up to \(n\). It is a discrete distribution:

\[ P(X = x) = \binom{n}{x} p^{x} (1 - p)^{n - x} \]

The other three statements are the conditions of a binomial experiment: a fixed number of independent trials, each with only two outcomes (success or failure), and the same probability of success \(p\) on every trial.

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