Business Stats
A measure of goodness of fit for the estimated regression equation is the: a) multiple coefficient of determination b) mean square due to error c) mean square due to regression d) sample size
A
Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y - Y-bar)(X - x-bar ) = -8 Σ (X - x-bar)^2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The point estimate of Y when X = -3 is a) 14 b) 0 c) 11 d) 8
A
Exhibit 12-9 A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). n = 10 ΣX = 90 ΣY = 170 Σ (Y -)(X - ) = = 466 Σ (Y - )2 = = 1434 Σ (X - )2 = 234 SSE = 505.98 Refer to Exhibit 12-9. The least squares estimate of b0 equals: a) -0.923 b) 0.923 c) -1.991 d) 1.991
A
Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. y-hat=170+34x1-3x2+8x3+58x4+3x5 For this model, SSR = 1,740 and SST = 2,000. Refer to Exhibit 13-10. The degrees of freedom associated with SSR are: a) 5 b) 6 c) 19 d) 24
A
Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 X1 20 5 X2 -18 6 X3 4 4 Refer to Exhibit 13-11. The estimated regression equation is: Question 22 options are in the attached photo.
A
Exhibit 13-12 In a laboratory experiment, data were gathered on the life span (Y in months) of 33 rats, units of daily protein intake (X1), and whether or not agent X2 (a proposed life extending agent) was added to the rats diet (X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed. y-hat=36+.8x1-1.7x2 Also provided are SSR = 60 and SST = 180. Refer to Exhibit 13-12. The degrees of freedom associated with SSE are: a) 30 b) 3 c) 33 d) 32
A
Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations. Coefficient Standard Error Constant 12.924 4.425 X1 -3.682 2.630 X2 45.216 12.560 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Regression 4,853 Mean Square Regression 2,426.5 Error 485.3 F Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are: a) 2 b) 3 c) 13 d) 15
A
Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations: Coefficient Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Sum of Squares Regression - 4.853 Mean Square Regression - 2426.5 Error - 485.3 Refer to exhibit 13-6. We want to test whether the parameter Beta1 is significant. The test statistic equals: a) -1.4 b) 1.4 c) 3.6 d) 5
A
Exhibit 13-8* The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X1) and their gender (X2) (0 if male and 1 if female). y-hat=30+.7x1+3x2 Also provided are SST = 1,200 and SSE = 384. Refer to Exhibit 13-8. The multiple coefficient of determination is a) 0.68 b) 0.32 c) 0.42 d) 0.50
A
Exhibit 13-9 In a regression analysis involving 25 observations, the following estimated regression equation was developed. y-hat=10-18x1+3x2+14x3 Also, the following standard errors and the sum of squares were obtained. Sb1 = 3 Sb2 = 6 Sb3 = 7 SST = 4,800 SSE = 1,296 Refer to Exhibit 13-9. The p-value for testing the significance of the regression model is: a) less than 0.01 b) between 0.01 and 0.025 c) between 0.05 and 0.1 d) between 0.025 and 0.05
A
In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to a) one b) zero c) the total number of elements in the data set d) None of these alternatives is correct.
A
In constructing a frequency distribution, the approximate class width is computed as: a) (largest data value - smallest data value)/number of classes b) (largest data value - smallest data value)/sample size c) (smallest data value - largest data value)/sample size d) largest data value/number of classes
A
When data are positively skewed, the mean will usually be: a) greater than the median b) smaller than the median c) equal to the median d) positive
A
Which of the following is not a measure of dispersion? a) mode b) standard deviation c) range d) interquartile range
A
Exhibit 13-5 Below you are given a partial Minitab output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 X1 25.625 9.150 X2 -5.720 3.575 X3 0.823 0.183 Refer to Exhibit 13-5. The interpretation of the coefficient on X1 is that: a) a one unit change in X1 will lead to a 25.625 unit change in Y b) a one unit change in X1 will lead to a 25.625 unit increase in Y when all other variables are held constant c) a one unit change in X1 will lead to a 25.625 unit increase in X2 when all other variables are held constant d) It is impossible to interpret the coefficient.
B
Exhibit 13-7 A regression model is involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares. SSR-165 SSE=60 Refer to Exhibit 13-7. If we want to rest for the significance of the model at 95% confidence, the critical F-value(from the table) is: a) 3.06 b) 3.48 c) 3.34 d) 3.11
B
Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. Refer to Exhibit 7-3. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is: a) 0.4664 b) 0.9328 c) 0.0336 d) 0.0672
B
Exhibit 9-2 n = 64 x-bar = 50 s = 16 H0: μ >= 54 Ha: μ < 54 Refer to Exhibit 9-2. If the test is done at 95% confidence, the null hypothesis should: a) None of these alternatives is correct. b) be rejected c) Not enough information is given to answer this question. d) not be rejected
B
Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no." The point estimate of the proportion in the population who will respond "no" is: a) 75 b) 0.25 c) 0.75 d) 0.50
B
If the coefficient of determination is equal to 1, the the coefficient of correlation: a) must also be equal to 1 b) can be either -1 or 1 c) can be any value between -1 and 1 d) must be -1
B
In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is: a) 0.80 b) 0.90 c) 0.25 d) 0.15
B
In hypothesis testing, the tentative assumption about the population parameter is: a) the alternative hypothesis b) the null hypothesis c) either the null or the alternative d) None of these alternatives is correct.
B
The interval estimate of the mean value of y for a given value of x is: a) prediction interval estimate b) confidence interval estimate c) average regression d) x versus y correlation interval
B
The probability distribution of all possible values of the sample mean is: a) the probability density function of x-bar b) the sampling distribution of x-bar c) the grand mean, since it considers all possible values of the sample mean d) one, since it considers all possible values of the sample mean
B
The symbol o^2 is used to represent: a)the variance of the population b) the standard deviation of the sample c) the standard deviation of the population d) the variance of the sample
B
The t value for a 95% confidence interval estimation with 24 degrees of freedom is a) 1.711 b) 2.064 c) 2.492 d) 2.069
B
Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations. Coefficient Standard Error Constant 12.924 4.425 x1 -3.682 2.630 x2 45.216 12.560 Analysis of Variance Sum of Squares Regression- 4.853 Mean Square Regression - 2426.5 Error - 485.3 Refer to Exhibit 13-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals: a) 3.41 b) 3.63 c) 3.81 d) 19.41
C
Exhibit 7-3 In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. Refer to Exhibit 7-3. The standard deviation of , known as the standard error of the proportion is approximately a) 0.5477 b) 5.477 c) 0.05477 d) 54.77
C
If we consider the simple random sampling process as an experiment, the sample mean is: a) always zero b) always smaller than the population mean c) a random variable d) exactly equal to the population mean
C
In a multiple regression model, the values of the error term, E, are assumed to be: a) zero b) dependent on each other c) independent of each other d) always negative
C
In regression analysis, the unbiased estimate of the variance is: a) coefficient of correlation b) coefficient of determination c) mean square error d) slope of the regression equation
C
The median is a measure of a) relative dispersion b) absolute dispersion c) central location d) relative location
C
You are given the following info about y and x y - dependent variable 5 4 3 2 1 x - independent variable 1 2 3 4 5 Refer to Exhibit 12-2. The least squares estimate of b0 (intercept) equals: a) 1 b) -1 c) 6 d) 5
C
A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have: a) 18 degrees of freedom b) 200 degrees of freedom c) 199 degrees of freedom c) 181 degrees of freedom
D
A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is: a) 0.0568 b) 0.0778 c) 0.4222 d) 0.9222
D
A statistics professor asked students in a class their ages. On the basis of this information, the professor states that the average age of all the students in the university is 24 years. This is an example of: a): a census b) descriptive statistics c) an experiment d) statistical inference
D
An interval estimate is a range of values used to estimate a) the shape of the population's distribution b) the sampling distribution c) a sample statistic d) a population parameter
D
Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y - y-bar)(X - x-bar ) = -8 Σ (X - x-bar)^2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The Y intercept is: a) 0.0 b) -1 c) 1.0 d) 11
D
Exhibit 12-10 The following information regarding a dependent variable Y and an independent variable X is provided. n = 4 ΣX = 16 ΣY = 28 Σ (Y - y-bar)(X - x-bar) = -8 Σ (X - x-bar)^2 = 8 SST = 42 SSE = 34 Refer to Exhibit 12-10. The slope of the regression function is a) 0.0 b) 1.0 c) 11 d) -1
D
Exhibit 12-8 The following information regarding a dependent variable Y and an independent variable X is provided: n = 4 ΣX = 90 ΣY = 340 Σ (Y - y-bar)(X - x-bar) = -156 Σ (X - x-bar)^2 = 234 Σ (Y - y-bar)^2 = 1974 SSR = 104 Refer to Exhibit 12-8. The coefficient of correlation is: a) 0.2295 b) -0.0572 c) 0.0527 d) -0.2295
D
Exhibit 13-10 In a regression model involving 30 observations, the follwoing estimated regression equation was obtained. y-hat=170+34x1-3x2+8x3+58x4+3x5 Refer to Exhibit 13-10. The value of SSE is: a) 2000 b) 170 c) 3740 d) 260
D
Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 X1 20 5 X2 -18 6 X3 4 4 Refer to Exhibit 13-11. The critical t value obtained from the table to test an individual parameter at the 5% level is: a) 2.06 b) 2.069 c) 2.074 d) 2.080
D
Exhibit 13-5 Below you are given a partial Minitab output based on a sample of 25 observations. Coefficient Standard Error Constant 145.32 148.682 X1 25.62 59.150 X2 -5.720 3.575 X3 0.823 0.183 Refer to Exhibit 13-5. The t value obtained from the table to test an individual parameter at the 5% level is: a) 2.06 b) 2.069 c) 2.074 d) 2.080
D
Exhibit 13-9 In a regression analysis involving 25 observations, the following estimated regression equation was developed. y-hat=10-18x1+3x2+14x3 Also, the following standard errors and the sum of squares were obtained. Sb1=3 Sb2= 6 Sb3=7 SST=4800 SSE=1296 Refer to Exhibit 13-9. If we are interested in testing for the significant of the relationship among the variables (i.e. significance of the model) the critical value of F at a=.05 is: a) 3.10 b) 2.76 c) 2.78 d) 3.07
D
Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds? a) 28.82% b) 0.5762% c) 0.281% d) 57.62%
D
Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is: a) 7.04 to 110.96 hours b) 7.36 to 10.64 hours c) 7.80 to 10.20 hours d) 8.61 to 9.39 hours
D
Exhibit 8-5 A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. Refer to Exhibit 8-5. The margin of error at 95% confidence is: a) 1.998 b) 1400 c) 240 d) 59.95
D
Exhibit 8-6 A sample of 75 information system managers had an average hourly income of $40.75 with a standard deviation of $7.00.Refer to Exhibit 8-6. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is a) 1.96 b) 1.64 c) 1.28 d) 1.993
D
In a multiple regression analysis involving 15 independent variables and 200 observations. SST=800 and SSE=240. The coefficient of determination is: a) 0.300 b) 0.192 c) 0.500 d) 0.700
D
In multiple regression analysis, a) there can be any number of dependent variables but only one independent variable b) there must be only one independent variable c) the coefficient of determination must be larger than 1 d) there can be several independent variables, but only one dependent variable
D
In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are a) 47 and 3 b) 3 and 47 c) 2 and 43 d) 3 and 43
D
In regression analysis, if the independent variable is measured in pounds, the dependent variable: a) must also be in pounds b) must be in some unit of weight c) cannot be in pounds d) can be any units
D
In the following estimated regression equation y-hat=b0+b1x a) b1 is the intercept b) b0 is the slope c) None of these alternatives is correct d) b1 is the slope
D
Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. (mu)(fancy X)060-1.theta pi y= 50 + 8 X Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales (in dollars) is: a) $8,050 b) $130 c) $130,000 d) $1,300,000
D
Social security numbers consist of numeric values. Therefore, social security is an example of a) a quantitative variable b) either a quantitative or a categorical variable c) an exchange variable d) a categorical variable
D
The average age in a sample of 190 students at City College is 22. As a result of this sample, it can be concluded that the average age of all the students at City College: a) must be more than 22, since the population is always larger than the sample b) must be less than 22, since the sample is only a part of the population c) could not be 22 d) could be larger, smaller, or equal to 22
D
The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is: a) H0: μ 40,000 Ha: μ > 40,000 b) H0: μ 40,000 Ha: μ < 40,000 c) H0: μ < 40,000 Ha: μ 40,000 d) H0: μ > 40,000 Ha: μ 40,000
D
The measure of location which is the most likely to be influenced by extreme values in the data set is the a) range b) median c) mode d) mean
D
The ratio of MSE/MSR yields a) SST b) the F statistic c) SSR d) None of these alternatives is correct.
D
Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. y-hat= 170+34x1-3x2+8x3+58x4+3x5 For this model, SSR =1740 and SST= 2000 Refer to Exhibit 13-10. The degrees of freedom associated with SSE are: a) 19 b) 24 c) 6 d) 5
B
Exhibit 13-3 In a regression model involving 30 observations. the following estimated regression equation was obtained: y-hat=17+4x1-3x2+8x3+8x4 For this model SSR=700 and SSE=100. Refer to Exhibit 13-3. The conclusion is that the" a) slope of x2 is significant b) model is not significant c) model is significant d) slop of x1 is significant
C
A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 Refer to Exhibit 3-3. The coefficient of variation is a) 72.66% b) 81.24% c) 264% d) 330%
B
Doubling the size of the sample will a) reduce the standard error of the mean to one-half its current value b) reduce the standard error of the mean to approximately 70% of its current value c) have no effect on the standard error of the mean d) double the standard error of the mean
B
Exhibit 12-3 You are given the following information about y and x. y Dependent Variable 12 3 7 6 x Independent Variable 4 6 2 4 Refer to Exhibit 12-3. The least squares estimate of b1 equals: a) 1 b) -1 c) -11 d) 11
B
Exhibit 12-5 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 1 1 2 2 3 3 4 4 5 5 Refer to Exhibit 12-5. The least squares estimate of the Y intercept is: a) 1 b) 0 c) -1 d) 3
B
A frequency distribution is a tabular summary of data showing the a) fraction of items in several classes b) percentage of items in several classes c) relative percentage of items in several classes d) number of items in several classes
D
A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is: a) 0.0347 b) 0.7200 c) 0.9511 d) 8.3600
C
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation y-hat = 60 - 8X The above equation implies that an: a) increase of $1 in price is associated with a decrease of $8 in sales b) increase of $1 in price is associated with a decrease of $52 in sales c) increase of $1 in price is associated with a decrease of $8000 in sales d) increase of $8 in price is associated with an decrease of $52,000 in sales
C
A regression analysis involved 8 independent variables and 99 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have a) 98 degrees of freedom b) 97 degrees of freedom c) 90 degrees of freedom d) 7 degrees of freedom
C
A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the: a) approximation theorem b) normal probability theorem c) central limit theorem d) central normality theorem
C
Exhibit 12-1 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-1. The coefficient of determination is a) 0.7096 b) -0.7906 c) 0.625 d) 0.375
C
Exhibit 12-2 You are given the following information about y and x. y Dependent Variable 5 4 3 2 1 x Independent Variable 1 2 3 4 5 Refer to Exhibit 12-2. The sample correlation coefficient equals a) 0 b) +1 c) -1 d) -0.5
C
Exhibit 12-2 You are given the following information about y and x. y - Dependent Variable 5 4 3 2 1 x - Independent Variable 1 2 3 4 5 Refer to Exhibit 12-2. The point estimate of y when x = 10 is: a) -10 b) 10 c) -4 d) 4
C
Exhibit 13-12 In a lab experiment, data were gathered on the life span (Y in months) of 33 rates, units of daily protein intake(X1), and whether or not agent X2 (a proposed life extending agent) was added to the rats diet (X2=0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed. y-bar=36+.8x1-1.7x2 Also provided are SSR=60 and SST=180. Refer to Exhibit 13-12. From the above function, it can be said that the life expectancy of rates were given agent X2 is: a) .8 more than those who did not take agent X2 b) 1.7 more than those who did not take agent X2 c) 1.7 less than those who did not take agent X2 d) .8 less than those who did not take agent X2
C
Exhibit 13-2 A regression model between sales (Y in $1,000), unit price (X1 in dollars) and television advertisement (X2 in dollars) resulted in the following function: y-hat = 7=3x(little one) +5x(little 2) For this model SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 13-2. To test for the significance of the model, the test statistic F is: a) 1.75 b) 2.33 c) 17.5 d) .70
C
