Business Statistics and Operations Management Questions and Answers

Answer: B

Normal deviation is not a measure of dispersion.

Measures of dispersion show how spread out the values are around a central value. The standard ones are the range (the difference between the largest and smallest values), the quartile deviation, the mean deviation (the average of absolute deviations from the mean or median) and the standard deviation (the square root of the mean of the squared deviations from the mean), along with the variance and the coefficient of variation.

'Normal deviation' is not a statistical measure. The word normal belongs to the normal distribution, and the standard normal deviate (z) is a standardised score, not a measure of spread.

Answer: A

A type II error is accepting H₀ when it is false.

A hypothesis test can go wrong in two ways. A type I error is rejecting a null hypothesis that is true; its probability is the level of significance, α. A type II error is failing to reject (accepting) a null hypothesis that is false; its probability is β, and the power of the test is 1 − β.

Accepting H₀ when it is true and rejecting it when it is false are both correct decisions. Rejecting H₀ when it is true is the type I error.

Answer: B

Sampling error is reduced by increasing the sample size.

Sampling error is the difference between a sample statistic and the population value that arises because only part of the population is observed. Its size is measured by the standard error, which for a mean is \(\sigma/\sqrt{n}\), so it falls as the sample size n grows: quadrupling the sample halves the standard error.

Reducing the sample size does the opposite. Non-probability sampling does not reduce error; it makes it impossible to measure and adds the risk of bias. The size of the population is not under the researcher's control and hardly affects the error once the population is large.

Answer: D

The strongest correlation is r = −1.

The strength of a correlation is given by the absolute value of r, which runs from 0 (no linear relationship) to 1 (a perfect linear relationship). The sign gives only the direction: positive when the variables rise together, negative when one rises as the other falls. r = −1 is a perfect negative correlation, with all points exactly on a falling straight line.

r = 0 means no linear correlation, r = 0.25 a weak positive one, and r = 0.75 a fairly strong positive one, but all are weaker than |−1| = 1.

Answer: D

Equal variance of the residuals across predicted values is homoscedasticity.

Homoscedasticity is an assumption of linear regression: the spread of the residuals around the regression line should be the same at all levels of the predicted dependent variable. When the spread fans out or narrows as the predicted value changes, the data are heteroscedastic, and the standard errors of the coefficients become unreliable.

Normality is the assumption that the residuals are normally distributed. Multicollinearity is high correlation among the independent variables. Homogeneity (of variance) is the related assumption for comparing groups, as in ANOVA, not the regression term asked for.

Answer: D

It indicates that the problem has multiple optimal solutions.

In the optimality test of a transportation problem (the MODI or stepping-stone method), the opportunity cost of each empty (unoccupied) cell tells how the total cost would change if that cell were brought into the solution. If all are non-negative the solution is optimal. If some empty cell has an opportunity cost of exactly zero, it can be brought into the solution without changing the total cost, so there is at least one other optimal solution.

Degeneracy is a different condition: fewer occupied cells than m + n − 1. Nothing is wrong with the solution, and it remains feasible.

Answer: C

Process layout needs more space than product layout for the same output.

In a process (functional) layout, similar machines are grouped into departments and jobs move between them in different sequences. Material travels farther, work waits between operations, and room is needed for work-in-progress stocks and for aisles and handling, so floor space requirements are higher.

In a product (line) layout, machines are arranged in the sequence of operations for one product, material flows straight through and little work-in-progress builds up, so it uses space more economically. The space difference is well established, so it can be determined and is not equal.

Answer: B

The transportation approach to location aims to minimise total shipping costs.

When a firm chooses among candidate locations for a new plant or warehouse, the transportation method of linear programming is solved for each option to find the shipping pattern from sources to destinations that minimises the total cost of transporting the goods. The location that gives the lowest total shipping cost is preferred.

Total costs, total variable costs and fixed costs bring in production and facility costs that the transportation model does not optimise; they are weighed separately, for instance in break-even location analysis.

Answer: D

A dummy activity is necessary when two activities share the same starting and ending node.

In an activity-on-arrow network, each activity must be identified uniquely by its pair of start and end nodes. If two parallel activities ran between the same two nodes they would be indistinguishable, so a dummy activity, which takes no time or resources and is drawn as a dashed arrow, is inserted to give one of them a separate node. Dummies are also used to show a logical dependency that cannot be drawn otherwise.

Two activities may share a starting node, or an ending node, without any problem, as long as they do not share both, and a node not connecting to another is a drawing error rather than a reason for a dummy.

Answer: D

Changes in the country's price level are measured by the Wholesale price index number.

The wholesale price index measures the average change in the prices of goods traded in bulk across the whole economy, covering primary articles, fuel and manufactured products, so it is used as a measure of the general price level and inflation.

A cost of living index measures the change in the cost of a particular group's consumption basket, such as industrial workers. A production index measures changes in output, not prices, and a security price index measures share prices.