# MATHEMATICS

**46.** Using the hat matrix elements *h _{i}* to determine influential points in a multiple regression model with

*k*independent variable and

*n*observations,

*X*is an influential point if

_{i}[removed]A) *h _{i}* >

*n*(

*k*+ 1)/2

[removed]B)

*h*> 2(

_{i}*k*+ 1)/

*n*

[removed]C)

*h*<

_{i}*n*(

*k*+ 1)/2

[removed]D)

*h*< 2(

_{i}*k*+ 1)/

*n*

**47.** The method of least squares is used on time-series data for

[removed]A) obtaining the trend equation.

[removed]B) exponentially smoothing a series.

[removed]C) eliminating irregular movements.

[removed]D) deseasonalizing the data.

**48.**

TABLE 17-1

The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.

where: *S*1 is state of nature 1 *A*1 is action alternative 1

*S2* is state of nature 2 *A*2 is action alternative 2

*A*3 is action alternative 3

Referring to Table 17-1, if the probability of *S*1 is 0.5, then the coefficient of variation for *A*2 is

[removed]A) 2

[removed]B) 1.5

[removed]C) 0.231

[removed]D) 0.5

**49.** Which of the following is NOT one of Deming’s 14 points?

[removed]A) Award business on the basis of price tag alone.

[removed]B) Break down barriers between staff areas..

[removed]C) Create constancy of purpose for improvement of product or service.

[removed]D) Drive out fear.

**50.**

TABLE 11-2

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

ANOVA

Referring to Table 11-2, at a significance level of 1%,

[removed]A) there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.

[removed]B) there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.

[removed]C) there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.

[removed]D) there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.