Business Statistics and Operations Management Questions and Answers

Q: While solving a transportation problem by applying Vogel's approximation method to a profit maximisation problem, row and column penalties are determined by :

Penalties are found from the difference between the two highest unit costs in each row and column, the figures here being profits.In a minimisation problem, Vogel's method takes the difference between the two lowest costs in each row and column: the penalty for not using the cheapest cell. In a profit maximisation problem the best cell is the one with the highest profit, so the penalty is the profit lost by not using it, the difference between the highest and second highest values. Allocation then goes to the row or column with the largest penalty, in its highest-profit cell.The difference between the two lowest values is the rule for minimisation, and the single smallest or largest value is not a penalty at all. (Equivalently, the profit matrix can be converted into an opportunity loss matrix and solved as minimisation.)

Q: X bar charts discover assignable causes ........................ samples.

X bar charts discover assignable causes between samples.An X-bar chart plots the mean of each sample taken from a process over time. A shift in the process mean, from tool wear, a new batch of material or a change of operator, makes sample means differ from one another and fall outside the control limits. It therefore detects variation between samples.Variation within a sample, the spread among items taken at the same time, is monitored by the range (R) chart or the standard deviation chart, which is why X-bar and R charts are used together. 'Among' and 'inside' are not the standard terms.

Q: The decision based on inspection by variables is ................... reliable than by attributes.

Decisions based on inspection by variables are more reliable than those by attributes.Inspection by variables measures the actual value of a characteristic, such as a diameter in millimetres, while inspection by attributes only records whether each item is good or defective. A measurement carries far more information than a pass-or-fail mark, so for the same sample size variables inspection gives a more reliable decision, or the same reliability with a smaller sample.'Less' reverses the relationship. 'More than' and 'less than' do not fit the sentence, which already contains 'than'.

Q: The ....................... is a plan for the production of individual end items.

The plan is the MPS, the master production schedule.The master production schedule states which end items will be produced, in what quantities and in which periods. It translates the aggregate plan into a schedule for individual finished products and is the main input to MRP.MRP (material requirements planning) works backwards from the MPS through the bill of materials to plan components and raw materials, not end items. MRP II extends this to all manufacturing resources, including capacity and finance. JIT is a philosophy of producing just what is needed when it is needed, not a schedule of end items.

Q: A one tailed test :

A one tailed test is directional.In a one-tailed test the alternative hypothesis states the direction of the difference, for example \(H_{1}: \mu \gt \mu_{0}\) or \(H_{1}: \mu \lt \mu_{0}\), and the whole rejection region lies in one tail of the sampling distribution.A two-tailed test is the non-directional one, with \(H_{1}: \mu \neq \mu_{0}\) and rejection regions in both tails. One-tailed tests are not limited to the normal distribution: t, F and chi-square tests can also be one-tailed.

Q: The value of R2 .................

The value of R2 is between 0 and 1.R2, the coefficient of determination, is the proportion of the variation in the dependent variable explained by the regression:\[ R^{2} = 1 - \frac{SS_{res}}{SS_{tot}} \]As a proportion it cannot be negative or exceed 1: 0 means the model explains nothing and 1 that it explains everything. The range -1 to 1 belongs to the correlation coefficient r, whose square, in simple regression, is R2. A value always above 1, or from -2 to 2, is impossible.

Q: Opportunity loss refers to :

Opportunity loss is the difference between actual pay-off and optimal pay-off.In decision theory, the opportunity loss (regret) of an action under a given state of nature is the pay-off of the best action for that state minus the pay-off of the action actually chosen. It measures what was given up by not choosing the best course, and it is zero when the best action was chosen.It is not the expected value or expected loss of a bad decision, which are averages over states, and it is regret from choosing a less than optimal action, not from making no decision at all.

Q: Which one of the following is not part of calculation of EOQ ?

The item not used in calculating EOQ is the number of orders (N).The economic order quantity balances ordering and carrying costs:\[ EOQ = \sqrt{\frac{2AO}{C}} \]where A is the annual requirement, O the cost per order and C the carrying cost per unit per year. The number of orders is an output of the calculation, found afterwards as A divided by EOQ, not an input to it.

Q: By convention, which type of error is considered to be more serious ?

By convention, a Type I error is considered more serious.A Type I error is rejecting a null hypothesis that is true; a Type II error is failing to reject a false one. The conventional testing procedure fixes the probability of a Type I error in advance at a small level of significance (alpha, typically 5% or 1%) and then tries to minimise the Type II error, which shows that the Type I error is the one treated as more serious, as in the legal principle of not convicting an innocent person.The other options do not reflect this asymmetric convention.

Q: Which of the following is the most common queue discipline ?

The most common queue discipline is first come first served.Queue discipline is the rule by which waiting customers are chosen for service. First come, first served (FCFS or FIFO) is the one used at most ticket counters, banks and service desks, and it is the standard assumption in the basic queuing models.Other disciplines exist, such as last come first served, service in random order, priority rules, and in job scheduling the shortest processing time rule, but they are used in special situations. 'Shortest' and 'longest processing route' and 'minimum black time' are not standard queue disciplines.

While solving a transportation problem by applying Vogel's approximation method to a profit maximisation problem, row and column penalties are determined by :

A.Finding the smallest unit cost in each row or column
B.Finding the difference between the two highest unit costs in each row and column
C.Finding the difference between the two lowest unit costs in each row and column.
D.Finding the largest unit cost in each row or column.

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: B

Penalties are found from the difference between the two highest unit costs in each row and column, the figures here being profits.

In a minimisation problem, Vogel's method takes the difference between the two lowest costs in each row and column: the penalty for not using the cheapest cell. In a profit maximisation problem the best cell is the one with the highest profit, so the penalty is the profit lost by not using it, the difference between the highest and second highest values. Allocation then goes to the row or column with the largest penalty, in its highest-profit cell.

The difference between the two lowest values is the rule for minimisation, and the single smallest or largest value is not a penalty at all. (Equivalently, the profit matrix can be converted into an opportunity loss matrix and solved as minimisation.)

Discuss in Forum

X bar charts discover assignable causes ........................ samples.

A.between
B.within
C.among
D.inside

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

X bar charts discover assignable causes between samples.

An X-bar chart plots the mean of each sample taken from a process over time. A shift in the process mean, from tool wear, a new batch of material or a change of operator, makes sample means differ from one another and fall outside the control limits. It therefore detects variation between samples.

Variation within a sample, the spread among items taken at the same time, is monitored by the range (R) chart or the standard deviation chart, which is why X-bar and R charts are used together. 'Among' and 'inside' are not the standard terms.

Discuss in Forum

The decision based on inspection by variables is ................... reliable than by attributes.

A.Less
B.Less than
C.More
D.More than

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

Decisions based on inspection by variables are more reliable than those by attributes.

Inspection by variables measures the actual value of a characteristic, such as a diameter in millimetres, while inspection by attributes only records whether each item is good or defective. A measurement carries far more information than a pass-or-fail mark, so for the same sample size variables inspection gives a more reliable decision, or the same reliability with a smaller sample.

'Less' reverses the relationship. 'More than' and 'less than' do not fit the sentence, which already contains 'than'.

Discuss in Forum

The ....................... is a plan for the production of individual end items.

A.JIT
B.MRP II
C.MRP
D.MPS

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: D

The plan is the MPS, the master production schedule.

The master production schedule states which end items will be produced, in what quantities and in which periods. It translates the aggregate plan into a schedule for individual finished products and is the main input to MRP.

MRP (material requirements planning) works backwards from the MPS through the bill of materials to plan components and raw materials, not end items. MRP II extends this to all manufacturing resources, including capacity and finance. JIT is a philosophy of producing just what is needed when it is needed, not a schedule of end items.

Discuss in Forum

A one tailed test :

A.cannot be used in nominal distribution
B.is non-directional
C.is directional
D.is based on normal distribution only

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

A one tailed test is directional.

In a one-tailed test the alternative hypothesis states the direction of the difference, for example \(H_{1}: \mu \gt \mu_{0}\) or \(H_{1}: \mu \lt \mu_{0}\), and the whole rejection region lies in one tail of the sampling distribution.

A two-tailed test is the non-directional one, with \(H_{1}: \mu \neq \mu_{0}\) and rejection regions in both tails. One-tailed tests are not limited to the normal distribution: t, F and chi-square tests can also be one-tailed.

Discuss in Forum

The value of R² .................

A.is between -1 to 1
B.is always greater than 1
C.is between -2 to 2
D.is between 0 and 1

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: D

The value of R² is between 0 and 1.

R², the coefficient of determination, is the proportion of the variation in the dependent variable explained by the regression:

\[ R^{2} = 1 - \frac{SS_{res}}{SS_{tot}} \]

As a proportion it cannot be negative or exceed 1: 0 means the model explains nothing and 1 that it explains everything. The range -1 to 1 belongs to the correlation coefficient r, whose square, in simple regression, is R². A value always above 1, or from -2 to 2, is impossible.

Discuss in Forum

Opportunity loss refers to :

A.Expected value of a bad decision
B.Expected loss from a bad decision
C.Difference between actual pay-off and optimal pay-off
D.Regret from not having made a decision

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: C

Opportunity loss is the difference between actual pay-off and optimal pay-off.

In decision theory, the opportunity loss (regret) of an action under a given state of nature is the pay-off of the best action for that state minus the pay-off of the action actually chosen. It measures what was given up by not choosing the best course, and it is zero when the best action was chosen.

It is not the expected value or expected loss of a bad decision, which are averages over states, and it is regret from choosing a less than optimal action, not from making no decision at all.

Discuss in Forum

Which one of the following is not part of calculation of EOQ ?

A.Annual Requirement (A)
B.Per Order Cost (O)
C.Carrying Cost Per Unit (C)
D.Number of Orders (N)

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: D

The item not used in calculating EOQ is the number of orders (N).

The economic order quantity balances ordering and carrying costs:

\[ EOQ = \sqrt{\frac{2AO}{C}} \]

where A is the annual requirement, O the cost per order and C the carrying cost per unit per year. The number of orders is an output of the calculation, found afterwards as A divided by EOQ, not an input to it.

Discuss in Forum

By convention, which type of error is considered to be more serious ?

A.Type II
B.Type I
C.Neither Type I nor Type II
D.Both Type I and Type II

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: B

By convention, a Type I error is considered more serious.

A Type I error is rejecting a null hypothesis that is true; a Type II error is failing to reject a false one. The conventional testing procedure fixes the probability of a Type I error in advance at a small level of significance (alpha, typically 5% or 1%) and then tries to minimise the Type II error, which shows that the Type I error is the one treated as more serious, as in the legal principle of not convicting an innocent person.

The other options do not reflect this asymmetric convention.

Discuss in Forum

10.

Which of the following is the most common queue discipline ?

A.First come first served
B.Shortest processing route
C.Longest processing route
D.Minimum black time

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

The most common queue discipline is first come first served.

Queue discipline is the rule by which waiting customers are chosen for service. First come, first served (FCFS or FIFO) is the one used at most ticket counters, banks and service desks, and it is the standard assumption in the basic queuing models.

Other disciplines exist, such as last come first served, service in random order, priority rules, and in job scheduling the shortest processing time rule, but they are used in special situations. 'Shortest' and 'longest processing route' and 'minimum black time' are not standard queue disciplines.

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