# Mathematics

Q8. In a multiple regression model, the adjusted r^{2}

a. cannot be negative.

b. can sometimes be negative.

c. can sometimes be greater than +1.

d. has to fall between 0 and +1.

Q9. Why would you use the Tukey-Kramer procedure?

a. To test for normality.

b. To test for homogeneity of variance.

c. To test independence of errors.

d. To test for differences in pairwise means.

Q10. A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. How should the data be analyzed?

Starting Room | ||

Interior | Exterior | |

Wall Signs | 141 | 224 |

119 | 339 | |

238 | 139 | |

Map | 85 | 226 |

94 | 129 | |

126 | 130 |

a. Completely randomized design

b. Randomized block design

c. 2 x 2 factorial design

d. Kruskal-Wallis rank test

Q11. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is

Y_{i} = ß_{0} + ß_{1}x_{1i} + ß_{2}x_{2i} + ß_{3}x_{3i} + e_{i}

where

Y is the price per hour

x_{1} is a numerical variable = the number of blocks to the quadrangle

(Note that if x_{1} is less than 2, then the meter is on campus; if x_{1} is less than 3, then the meter is downtown)

x_{2} is a dummy variable = 1 if inside downtown and off campus, 0 otherwise

x_{3} is a dummy variable = 1 if outside downtown and off campus, 0 otherwise

The following Excel results are obtained.

Regression Statistics | |

Multiple R | 9.9659 |

R Square | 0.9331 |

Adjusted R Square | 0.9294 |

Standard Error | 0.0327 |

Observations | 58 |

ANOVA | df | SS | MS | F | Signif F |

Regression | 3 | 0.8094 | 0.2698 | 251.1995 | 1.0964E-31 |

Residual | 54 | 0.0580 | 0.0010 | ||

Total | 57 | 0.8675 |

Coeff | StdError | t Stat | P-value | |

Intercept | 0.5118 | 0.0136 | 37.4675 | 2.4904 |

X1 | -0.0045 | 0.0034 | -1.3275 | 0.1898 |

X2 | -0.2392 | 0.0123 | -19.3942 | 5.3581E-26 |

X3 | -0.0002 | 0.0123 | -0.0214 | 0.9829 |

Referring to the tables, predict the meter rate per hour if one parks outside of downtown and off campus, 3 blocks from the quad.

a. $-0.0139

b. $0.2589

c. $0.2604

d. $0.4981

Q12. If we use the chi-squared method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:

a. 3

b. 4

c. 5

d. 1

Q13. An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.

SUMMARY OUTPUT

Regression Statistics | |

Multiple R | 0.991 |

R Square | 0.982 |

Adjusted R Square | 0.976 |

Standard Error | 0.299 |

Observations | 10 |

ANOVA | df | SS | MS | F | Signif F |

Regression | 2 | 33.4163 | 16.7082 | 186.325 | 0.0001 |

Residual | 7 | 0.6277 | 0.0897 | ||

Total | 9 | 34.0440 |

Coeff | StdError | t Stat | P-value | |

Intercept | -0.0861 | 0.5674 | -0.152 | 0.8837 |

GDP | 0.7654 | 0.0574 | 13.340 | 0.0001 |

Price | -0.0006 | 0.0028 | -0.219 | 0.8330 |

Referring to the tables, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?

a. $4.39 billion

b. $0.39 billion

c. -$0.39 billion

d. -$1.33 billion

Q14. Testing for the existence of correlation is equivalent to

a. testing for the existence of the slope (β_{1}).

b. testing for the existence of the Y-intercept (β_{0}).

c. the confidence interval estimate for predicting Y.

d. testing for the existence of the slope (β_{10}).

Q15. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is

Y_{i} = ß_{0} + ß_{1}x_{1i} + ß_{2}x_{2i} + ß_{3}x_{3i} + e_{i}

where

Y is the price per hour

x_{1} is a numerical variable = the number of blocks to the quadrangle

(Note that if x_{1} is less than 2, then the meter is on campus; if x_{1} is less than 3, then the meter is downtown)

x_{2} is a dummy variable = 1 if inside downtown and off campus, 0 otherwise

x_{3} is a dummy variable = 1 if outside downtown and off campus, 0 otherwise

The following Excel results are obtained.

Regression Statistics | |

Multiple R | 9.9659 |

R Square | 0.9331 |

Adjusted R Square | 0.9294 |

Standard Error | 0.0327 |

Observations | 58 |

ANOVA | df | SS | MS | F | Signif F |

Regression | 3 | 0.8094 | 0.2698 | 251.1995 | 1.0964E-31 |

Residual | 54 | 0.0580 | 0.0010 | ||

Total | 57 | 0.8675 |

Coeff | StdError | t Stat | P-value | |

Intercept | 0.5118 | 0.0136 | 37.4675 | 2.4904 |

X1 | -0.0045 | 0.0034 | -1.3275 | 0.1898 |

X2 | -0.2392 | 0.0123 | -19.3942 | 5.3581E-26 |

X3 | -0.0002 | 0.0123 | -0.0214 | 0.9829 |

Referring to the tables, if one is already outside of downtown and off campus but decides to park an additional 3 blocks from the quadrangle, the estimated average parking meter rate will:

a. decrease by 0.0045.

b. decrease by 0.0135.

c. decrease by 0.0139.

d. decrease by 0.4979.

Q16. The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.

Hypothesized Difference0

Level of Significance 0.05

Group 1

Number of Successes163

Sample Size227

Group 2

Number of Successes154

Sample Size262

Group 1 Proportion0.718061674

Group 2 Proportion0.58778626

Difference in Two Proportions 0.130275414

Average Proportion0.648261759

Test Statistic3.00875353

Two-Tailed Test

Lower Critical Value -1.959961082

Upper Critical Value 1.959961082

p-Value 0.002623357

Referring to the data above, if you want to test the claim that “Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2),” the p-value of the test will be

a. 0.00262

b. 0.00262/2

c. 2*(0.00262)

d. 1 – (0.00262/2)