# MATHEMATICS

**40.** Blossom’s Flowers purchases roses for sale for Valentine’s Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine’s Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine’s Day: 100, 200, or 400 dozen roses. Given 0.2, 0.4, and 0.4 are the probabilities for the sale of 100, 200, or 400 dozen roses, respectively, then the *EMV* for buying 200 dozen roses is

[removed]A) $4,500

[removed]B) $1,700

[removed]C) $1,000

[removed]D) $2,500

**41.** Maintaining the gains that have been made with a revised process in the long term by avoiding potential problems that can occur when a process is changed involves which part of the DMAIC process?

[removed]A) Define

[removed]B) Measure

[removed]C) Analyze

[removed]D) Improve

[removed]E) Control

**42.** TABLE 11-3

A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3

B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7

Interpret the results of the analysis summarized in the following table:

Referring to Table 11-3, the within-group mean squares is

[removed]A) 0.29.

[removed]B) 0.10.

[removed]C) 1.18.

[removed]D) 1.06.

**43.**TABLE 12-7

The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day’s riders and finds the following:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

Referring to Table 12-7, the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same. Which test should she use?

[removed]A) *χ*^{2}-test for difference in proportions

[removed]B) Wilcoxon rank sum test

[removed]C) McNemar test for difference in proportions

[removed]D) Z-test for difference in proportions

**44.** The coefficient of determination (*r*^{2}) tells us

[removed]A) the proportion of total variation that is explained.

[removed]B) whether *r* has any significance.

[removed]C) that we should not partition the total variation.

[removed]D) that the coefficient of correlation (*r*) is larger than 1.

**45.**

TABLE 14-16

The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.

Following is the multiple regression output with *Y* = % *Passing* as the dependent variable, *X*_{1} = % *Attendance*, *X*_{2} = *Salaries* and *X*_{3} = *Spending*:

ANOVA

Referring to Table 14-16, which of the following is the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

[removed]A) *H*_{1} : At least one of β*j* ≠ 0 for *j* = 1, 2, 3

[removed]B) *H*_{1} : β_{0} = β_{1} = β_{2} = β_{3} ≠ 0

[removed]C) *H*_{1} : At least one of β*j* ≠ 0 for *j* = 0, 1, 2, 3

[removed]D) *H*_{1} : β_{1} = β_{2} = β_{3} ≠ 0