Unit 4 Business Stats

In a simple linear regression model, if the points on a scatter diagram lie on a straight line with a negative slope, which of the following is the coefficient of determination? Multiple Choice −1 0 +1 Infinity

+1

A sample regression equation is given by yˆ = −100 + 0.5x. If x = 20, the predicted value of y is ________. Multiple Choice −80 −90 110 120

-90

If there are five treatments under study, the number of pairwise comparisons is _______. Multiple Choice 15 5 20 10

10

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 32 20 25 9 Black 35 10 25 5 Hispanic 32 15 13 2 Asian 10 11 10 0 The row total for Asians is _____. Multiple Choice 86 75 62 31

31

A manager at a local bank analyzed the relationship between monthly salary (y, in $) and length of service (x, measured in months) for 30 employees. She estimates the following model: Salary = β0 + β1 Service + ε. The following table summarizes a portion of the regression results. Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 784.92 322.25 124.95 1,444.89 Service 9.19 3.20 2.64 15.74 Using the 95% confidence interval, which of the following is the conclusion to the following hypothesis test: H0:β0 = 0; HA: β0 ≠ 0? Multiple Choice At the 5% significance level, reject H0 because the interval contains 0. At the 5% significance level, do not reject H0 because the interval contains 0. At the 5% significance level, reject H0 because the interval does not contain 0. At the 5% significance level, do not reject H0 because the interval does not contain 0.

At the 5% significance level, reject H0 because the interval does not contain 0.

Suppose you want to determine if gender and major are independent. Which of the following tests should you use? Goodness-of-fit test for a multinomial experiment Chi-square test for independence Goodness-of-fit test for normality Jarque-Bera test for normality

Chi-square test for independence

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 32 20 25 9 Black 35 10 25 5 Hispanic 32 15 13 2 Asian 10 11 10 0 Which of the following is a way to ensure all expected frequencies in each cell of the above table are five or more? Multiple Choice Combine the expected frequencies for races Black and Hispanic. Combine the expected frequencies for races Hispanic and Asian. Combine the expected frequencies for seniorities Manager and Director. Remove the expected frequencies for the Director seniority.

Combine the expected frequencies for seniorities Manager and Director.

What is the name of the variable that is used to predict another variable? Multiple Choice Response Explanatory Coefficient of determination Standard error of the estimate

Explanatory

One-way ANOVA assumes the population standard deviations are unknown and assumed unequal. True or False

False

One-way ANOVA is used to determine if differences exist between the means of three or more populations under dependent sampling. True or False

False

The between-treatments variance is the estimate of σ2 based on the variability due to chance. True or False

False

A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South(4) sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. Source of Variation SS df MS F Between groups 87.79 3 29.26 9.12 Within groups 64.17 20 3.21 Total 151.96 23 The competing hypotheses about the mean crime rates are _______. Multiple Choice H0: μ1 = μ2 = μ3, HA: Not all population means are equal H0: Not all population means are equal, HA: μ1 = μ2 = μ3 H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal H0: Not all population means are equal, HA: μ1 = μ2 = μ3 = μ4

H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. Houston Charlotte Tucson Akron 45 25 25 10 65 30 30 15 105 35 19 15 55 10 30 10 85 50 10 5 90 70 35 10 x¯i 74.167 36.667 24.833 10.833 s2i 524.167 436.667 82.167 14.167 The competing hypotheses about the mean commute times are _______. Multiple Choice H0: μ1 = μ2 = μ3, HA: Not all population means are equal H0: Not all population means are equal, HA: μ1 = μ2 = μ3 H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal H0: Not all population means are equal, HA: μ1 = μ2 = μ3 = μ4

H0: μ1 = μ2 = μ3 = μ4, HA: Not all population means are equal

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________. Multiple Choice H0:β1 = 0 H0:β1 = 1 H0:b1 = 0 H0:b1 = 1

H0:β1 = 0

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 40.10 14.08 2.848 0.0052 Advertising 2.88 1.52 −1.895 0.0608 Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales? Multiple Choice H0:b1 = 0; HA:b1 ≠ 0. H0:b1 = 2.88; HA:b1 ≠ 2.88. H0:β1 = 0; HA:β1 ≠ 0. H0:β1 ≠ 0; HA:β1 = 0.

H0:β1 = 0; HA:β1 ≠ 0.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ________. Multiple Choice H0:β1 = 0 H0:β1 = 1 H0:b1 = 0 H0:b1 = 1

H0:β1 = 1

A sports analyst wants to exam the factors that may influence a tennis player's chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model: Win = β0 + β1 Double Faults + β2 Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table. df SS MS F Significance F Regression 2 1.24 0.620 41.85 5.34E-09 Residual 27 0.40 0.015 Total 29 1.64 Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 0.451 0.080 5.646 5.4E-06 0.287 0.614 Double Faults −0.007 0.0024 −2.875 0.0078 −0.012 −0.002 Aces 0.015 0.003 4.65 7.8E-05 0.008 0.023 When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________. Multiple Choice H0:β1 = β2 = 0 H0:β1 + β2 = 0 H0:β0 = β1 = β2 = 0 H0:β0 + β1 + β2 + 0

H0:β1 = β2 = 0

Which of the following statements about regression analysis is FALSE? Multiple Choice It uses information on the explanatory variables to predict the value of the response variable. It can establish cause-and-effect relationships. It is related to correlation analysis. It can have multiple explanatory variables.

It can establish cause-and-effect relationships.

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Coefficients Standard Error t-stat p-value Intercept 0.083 3.56 0.02 0.9822 x 1.417 0.63 2.25 0.0745 Is x significantly related to y at the 5% significance level? Multiple Choice Yes, because the p-value of 0.0745 is greater than 0.05. No, because the p-value of 0.0745 is greater than 0.05. Yes, because the slope coefficient of 1.417 is less than the test statistic of 2.25. No, because the slope coefficient of 1.417 is less than the test statistic of 2.25.

No, because the p-value of 0.0745 is greater than 0.05.

Which of the following is the assumption that is not applicable for a one-way ANOVA test? Multiple Choice The populations are normally distributed. The population standard deviations are not all equal. The samples are selected independently. The sample is drawn at random from each population.

The population standard deviations are not all equal.

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. True or False

True

Consider the following simple linear regression model: y = β0 + β1 + ε. The response variable is y Correct x ε β0

Y

The chi-square test of a contingency table is valid when the expected cell frequencies are equal to 0 more than 0 but less than 5 at least 5 negative

at least 5

The variability due to chance, also known as the within-treatments variance, is the estimate of σ2 which is not based on the variability _______. Multiple Choice between the sample means due to random chance within each sample due to the common population variance

between the sample means

Consider the following sample regression equation yˆ y^⁢ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ________. Multiple Choice increase by 60 decrease by 60 decrease by 60,000 increase by 60,000

decrease by 60,000

Excel and virtually all other statistical packages report the p-value ________. Multiple Choice for a two-tailed test that assesses whether the regression coefficient differs from one for a right-tailed test that assesses whether the regression coefficient is greater than zero for a two-tailed test that assesses whether the regression coefficient differs from zero for a left-tailed test that assesses whether the regression coefficient is less than zero

for a two-tailed test that assesses whether the regression coefficient differs from zero

When two regression models applied on the same data set have the same response variable but a different number of explanatory variables, the model that would evidently provide the better fit is the one with a ________. Multiple Choice lower standard error of the estimate and a higher coefficient of determination higher standard error of the estimate and a higher coefficient of determination higher coefficient of determination and a lower adjusted coefficient of determination lower standard error of the estimate and a higher adjusted coefficient of determination

lower standard error of the estimate and a higher adjusted coefficient of determination

iffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 0.0198 0.010 1.98 0.0598 −0.0008 0.0405 RM − Rf 1.827 0.191 9.58 1.494E-13 1.4456 2.2094 When testing whether there are abnormal returns, the conclusion to the test is at the 5% significance level is to ________. Multiple Choice reject H0; we can conclude there are abnormal returns not reject H0; we can conclude there are abnormal returns reject H0; we cannot conclude there are abnormal returns not reject H0, we cannot conclude there are abnormal returns

not reject H0, we cannot conclude there are abnormal returns

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β0 + β1 Leverage + ε. A 5% level of significance is used to study if leverage has a significant influence on returns. The value of the test statistic for the regression coefficient of Leverage is calculated as t198 = −1.09, with an associated p-value of 0.2770. The correct decision is to ________. Multiple Choice reject the null hypothesis; we can conclude that leverage significantly explains returns reject the null hypothesis; we cannot conclude that leverage significantly explains returns not reject the null hypothesis; we cannot conclude that leverage significantly explains returns not reject the null hypothesis; we can conclude that leverage significantly explains returns

not reject the null hypothesis; we cannot conclude that leverage significantly explains returns

The R2 of a multiple regression of y on x1 and x2 measures the ________. Multiple Choice percentage of the variation in y that is explained by the variability of x1 percentage of the variation in y that is explained by the variability of x2 statistical significance of the coefficients in the sample regression equation percentage of the variation in y that is explained by the sample regression equation

percentage of the variation in y that is explained by the sample regression equation

The one-way ANOVA null hypothesis is rejected when the _______. Multiple Choice two estimates of the variance are relatively close together variability in the sample means can be explained by chance ratio of the within-treatments variance and the between-treatments variance is 1 ratio of the within-treatments variance and the between-treatments variance is significantly greater than 1

ratio of the within-treatments variance and the between-treatments variance is significantly greater than 1

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. df SS MS F Significance F Regression 3 453 151 5.03 0.0030 Residual 85 2,521 30 Total 88 2,974 Coefficients Standard Error t-stat p-value Intercept 14.96 3.08 4.86 0.0000 x1 0.87 0.29 3.00 0.0035 x2 0.46 0.22 2.09 0.0400 x3 0.04 0.34 0.12 0.9066 When testing whether the explanatory variables are jointly significant at the 5% significance level, the conclusion is to ________. Multiple Choice reject H0, and conclude that the explanatory variables are jointly significant not reject H0, and conclude that the explanatory variables are jointly significant reject H0, and cannot conclude that the explanatory variables are jointly significant not reject H0, and cannot conclude that the explanatory variables are jointly significant

reject H0, and conclude that the explanatory variables are jointly significant

The between-treatments variance is based on a weighted sum of squared differences between the _______. Multiple Choice population variances and the overall mean of the data set sample means and the overall mean of the data set sample variances and the overall mean of the data set population means and the overall mean of the data set

sample means and the overall mean of the data set

Simple linear regression analysis differs from multiple regression analysis in that ________. Multiple Choice simple linear regression uses only one explanatory variable the coefficient of correlation is meaningless in simple linear regression goodness-of-fit measures cannot be calculated with simple linear regression the coefficient of determination is always higher in simple linear regression

simple linear regression uses only one explanatory variable

For the chi-square test of a contingency table, the expected cell frequencies are found as eij=(Row i total)(Column j total)Sample sizeeij=(Row⁢ i⁢ total)(Column⁢ j⁢ total)Sample⁢ size which is the same as the observed cell frequencies the cell probability multiplied by the sample size the row total the column total

the cell probability multiplied by the sample size

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. Houston Charlotte Tucson Akron 45 25 25 10 65 30 30 15 105 35 19 15 55 10 30 10 85 50 10 5 90 70 35 10 x¯i 74.167 36.667 24.833 10.833 s2i 524.167 436.667 82.167 14.167 Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is _______. Multiple Choice the populations are normally distributed. the population standard deviations are assumed to be equal. the samples are independent. the samples are not normally distributed.

the population standard deviations are assumed to be equal.

Consider the following sample regression equation yˆy^ = 150 − 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ________. Multiple Choice the price of Product A increases by $1, then we predict the demand to decrease 20 the price of Product A increases by $1, then we predict the demand to increase by 20 the price of Product A increases by $1, then we predict the demand to decrease by 20,000 the price of Product A increases by $1, then we predict the demand to increase by 20,000

the price of Product A increases by $1, then we predict the demand to decrease by 20,000

Consider the following sample regression equation yˆ y^⁢ = 200 + 10x, where y is the supply for Product A (in 1,000s) and x is the price of Product A (in $). The slope coefficient indicates that if ________. Multiple Choice the price of Product A increases by $1, then we predict the supply to decrease by 10 the price of Product A increases by $1, then we predict the supply to increase by 10 the price of Product A increases by $1, then we predict the supply to decrease by 10,000 the price of Product A increases by $1, then we predict the supply to increase by 10,000

the price of Product A increases by $1, then we predict the supply to increase by 10,000

For the chi-square test of a contingency table, the expected cell frequencies are found as the row total multiplied by the column total divided by the sample size the observed cell frequency (r−1)(c−1) rc

the row total multiplied by the column total divided by the sample size

The standard error of the estimate measures ________. Multiple Choice the variability of the explanatory variables the variability of the values of the sample regression coefficients the variability of the observed y-values around the predicted y-values the variability of the predicted y-values around the mean of the observed y-values

the variability of the observed y-values around the predicted y-values

The chi-square test of a contingency table is a test of independence for a single qualitative variable two qualitative variables two quantitative variables three or more quantitative variables

two qualitative variables

The coefficient of determination R2 is ________. Multiple Choice sometimes negative always lower than adjusted R2 usually higher than adjusted R2 always equal to adjusted R2

usually higher than adjusted R2

Consider the following simple linear regression model: y = β0 + β1x + ε. The explanatory variable is ________. Multiple Choice y x ε β0

x

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. df SS MS F Significance F Regression 3 453 151 5.03 0.0030 Residual 85 2,521 30 Total 88 2,974 Coefficients Standard Error t-stat p-value Intercept 14.96 3.08 4.86 0.0000 x1 0.87 0.29 3.00 0.0035 x2 0.46 0.22 2.09 0.0400 x3 0.04 0.34 0.12 0.9066 At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant? Multiple Choice Only x1 Only x3 x1 and x2 x2 and x3

x1 and x2

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate? Multiple Choice −1 0 +1 Infinity

0

In the following table, individuals are cross-classified by their age group and income level. Income Age Low Medium High 21-35 120 100 75 36-50 150 160 100 51-65 160 180 160 Which of the following is the estimated joint probability for the "low income and 21-35 age group" cell? Multiple Choice 0.0830 0.0874 0.0996 0.1328

0.0996

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Male Female Candidate A 150 130 Candidate B 100 120 For the chi-square test of independence, the assumed degrees of freedom are 1 2 3 4

1

The following is an incomplete ANOVA table. Source of Variation SS df MS F Between groups 2 12.5 Within groups Total 100 10 The value of the test statistic is _______. Multiple Choice 1.333 9.375 12.5 100

1.333

In the following table, individuals are cross-classified by their age group and income level. Income Age Low Medium High 21-35 120 100 75 36-50 150 160 100 51-65 160 180 160 Assuming age group and income are independent, the expected "low income and 21-35 age group" cell frequency is ________. Multiple Choice 105.27 107.72 146.31 178.42

105.27

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 32 20 25 9 Black 35 10 25 5 Hispanic 32 15 13 2 Asian 10 11 10 0 The column total for directors is _____. Multiple Choice 16 56 73 109

16

The following is an incomplete ANOVA table. Source of Variation SS df MS F Between groups 2 12.5 Within groups Total 100 10 The sum of squares due to treatments is _______. Multiple Choice 10 25 75 100

25

Consider the following sample regression equation yˆy^ = 200 + 10x, where y is the supply for Product A (in 1,000s) and x is the price of Product A (in $). If the price of Product A is $5, then we expect supply to be ________. Multiple Choice 250 2,500 25,000 250,000

250,000

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class Less than 650 650-750 More than 750 Income < $50,000 26 30 24 $50,000 ≤ Income < $100,000 63 53 44 $100,000 ≤ Income < $150,000 40 30 30 Income ≥ $150,000 21 17 22 The expected number of individuals with income less than $50,000 and a credit score between 650 and 750 is ______. Multiple Choice 24.0 26.0 32.5 52.0

26

A police chief wants to determine if crime rates are different for four different areas of the city (East(1), West(2), North(3), and South sides), and obtains data on the number of crimes per day in each area. The one-way ANOVA table is shown below. Source of Variation SS df MS F Between groups 87.79 3 29.26 9.12 Within groups 64.17 20 3.21 Total 151.96 23 The degrees of freedom for the hypothesis test are _______. Multiple Choice 4, 20 3, 23 3, 20 4, 23

3, 20

Consider the partially completed one-way ANOVA summary table. Source of Variation SS df MS F Between groups 270 Within groups 18 Total 810 21 The value of the test statistic is ________. Multiple Choice 3.0 2.2 5.5 7.4

3.0

In the following table, individuals are cross-classified by their age group and income level. Income Age Low Medium High 21-35 120 100 75 36-50 150 160 100 51-65 160 180 160 For the chi-square test of independence, the degrees of freedom are __________. Multiple Choice 2 4 9 8

4

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class Less than 650 650-750 More than 750 Income < $50,000 26 30 24 $50,000 ≤ Income < $100,000 63 53 44 $100,000 ≤ Income < $150,000 40 30 30 Income ≥ $150,000 21 17 22 The degrees of freedom for the critical value is ________. Multiple Choice 3 4 5 6

6

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 32 20 25 9 Black 35 10 25 5 Hispanic 32 15 13 2 Asian 10 11 10 0 For the chi-square test for independence to be valid, Martha combines the seniorities Manager and Director. As a result, the degrees of freedom used are _____. Multiple Choice 2 16 3 6

6

Suppose Bank of America would like to investigate if the credit score and income level of an individual are independent of one another. Bank of America selected a random sample of 400 adults and asked them to report their credit score range and their income range. The following contingency table presents these results. Credit Score Class Less than 650 650-750 More than 750 Income < $50,000 26 30 24 $50,000 ≤ Income < $100,000 63 53 44 $100,000 ≤ Income < $150,000 40 30 30 Income ≥ $150,000 21 17 22 The expected number of individuals with income between $50,000 and $100,000 and a credit score less than 650 is ________. Multiple Choice 30.0 32.5 37.5 60.0

60

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 56.1772 5.2145 10.7732 0.0000 Age 0.2845 0.0871 3.2671 0.0035 Which of the following is the estimate of Happiness for the person who is 65 years old? Multiple Choice 75 62 78 68

75

The following is an incomplete ANOVA table. Source of Variation SS df MS F Between groups 2 12.5 Within groups Total 100 10 For the within groups category, the degrees of freedom are _______. Multiple Choice 6 7 8 9

8

AutoTrader.com would like to test if a difference exists in the age of three different types of vehicles currently on the road: trucks, cars, and vans. The following data represent the age of a random sample of trucks, cars, and vans. Trucks Cars Vans 12 8 3 8 7 7 9 10 6 11 7 8 The grand mean for these observations is ________. Multiple Choice 7.2 8.0 8.9 9.3

8.0

The following is an incomplete ANOVA table. Source of Variation SS df MS F Between groups 2 12.5 Within groups Total 100 10 The mean square error is _______. Multiple Choice 1.333 9.375 25 75

9.375

Consider the sample regression equation yˆ = 12 + 3x1 − 5x2 + 7x3 − 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y? Multiple Choice Decrease by 2 Decrease by 4 Decrease by 7 No change in predicted y

Decrease by 7

Which of the following statements is TRUE about goodness-of-fit measures? Multiple Choice Goodness-of-fit measures are used to gauge the predictive power of a regression model. Goodness-of-fit measures are always improved by increasing the number of explanatory variables in a regression model. The higher the value of any goodness-of-fit measure, the better the model fit. Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.

Goodness-of-fit measures are used to assess how well the explanatory variables explain the variation in the response variable.

In the following table, individuals are cross-classified by their age group and income level. Income Age Low Medium High 21-35 120 100 75 36-50 150 160 100 51-65 160 180 160 To test that age group and income are independent, the null and alternative hypothesis are _________________________________________________________________________. Multiple Choice H0: Age group and income are dependent; HA: Age group and income are independent H0: Age group and income are mutually exclusive; HA: Age group and income are not mutually exclusive H0: Age group and income are not mutually exclusive; HA: Age group and income are mutually exclusive H0: Age group and income are independent; HA: Age group and income are dependent

H0: Age group and income are independent; HA: Age group and income are dependent

In the following table, likely voters' preferences of two candidates are cross-classified by gender. Male Female Candidate A 150 130 Candidate B 100 120 To test that gender and candidate preference are independent, the null hypothesis is H0: Gender and candidate preference are independent H0: Gender and candidate preference are mutually exclusive H0: Gender and candidate preference are not mutually exclusive H0: Gender and candidate preference are dependent

H0: Gender and candidate preference are independent

The following table shows the distribution of employees in an organization. Martha Foreman, an analyst, wants to see if race has a bearing on the position a person holds with this company. Seniority Race Coordinator Analyst Manager Director White 32 20 25 9 Black 35 10 25 5 Hispanic 32 15 13 2 Asian 10 11 10 0 To test that race and seniority are independent, the null and alternative hypothesis are _______________________________________________________________________. Multiple Choice H0: Race and seniority are independent; HA: Race and seniority are dependent H0: Race and seniority are mutually exclusive; HA: Race and seniority are not mutually exclusive H0: Race and seniority are not mutually exclusive; HA: Race and seniority are mutually exclusive H0: Race and seniority are dependent; HA: Race and seniority are independent

H0: Race and seniority are independent; HA: Race and seniority are dependent

Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 0.0198 0.010 1.98 0.0598 −0.0008 0.0405 RM − Rf 1.827 0.191 9.58 1.494E-13 1.4456 2.2094 You would like to determine whether an investment in Tiffany's is riskier than the market. When conducting this test, you set up the following competing hypotheses: ________. Multiple Choice H0:α = 0; HA:α ≠ 0 H0:β = 0; HA:β ≠ 0 H0:α ≤ 1; HA:α > 1 H0:β ≤ 1; HA:β > 1

H0:β ≤ 1; HA:β > 1

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β0 + β1Age + ε. The following table summarizes a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 56.1772 5.2145 10.7732 0.0000 Age 0.2845 0.0871 3.2671 0.0035 When defining whether age is significant in explaining happiness, the competing hypotheses are ________. Multiple Choice H0:β1 = 1; HA:β1 ≠ 1 H0:β1 = 0; HA:β1 ≠ 0 H0:β1 ≤ 0; HA:β1 > 0 H0:b1 ≥ 1; HA:β1 < 1

H0:β1 = 0; HA:β1 ≠ 0

A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x1), the number of bathrooms (x2), and its square footage (x3). She estimates the following model: Rent = β0 + β1 Bedroom + β2 Bath + β3Sqft + ε. The following table shows a portion of the regression results. df SS MS F Significance F Regression 3 5,694,717 1,898,239 50.88 4.99E-13 Residual 36 1,343,176 37,310 Total 39 7,037,893 Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 300 84.0 3.57 0.0010 130.03 470.79 Bedroom 226 60.3 3.75 0.0006 103.45 348.17 Bath 89 55.9 1.59 0.1195 −24.24 202.77 Sq ft 0.2 0.09 2.22 0.0276 0.024 0.39 When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________. Multiple Choice H0: β0 = β1 = β2 = β3 = 0 H0:β1 = β2 = β3 = 0 H0: β0 + β1 + β2 + β3 = 0 H0:β1 + β2 + β3 + 0

H0:β1 = β2 = β3 = 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________. Multiple Choice HA:β1 = 0 HA:β1 > 0 HA:β1 < 0 HA:b1 > 0

HA:β1 < 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________. Multiple Choice HA:β1 = 0 HA:β1 > 0 HA:β1 < 0 HA:b1 > 1

HA:β1 > 0

Which of the following statements is TRUE about tests of significance to determine whether there is evidence of a linear relationship between the response variable and the explanatory variables? Multiple Choice The test of individual significance is about whether there is evidence that at least one explanatory variable influences the response variable. The test of individual significance uses a right-tailed F test. The test of individual significance is the same as the test of joint significance for a simple linear regression model. The test of joint significance uses a two-tailed test

The test of individual significance is the same as the test of joint significance for a simple linear regression model.

Which of the following is an example in which a one-way ANOVA test is appropriate? Multiple Choice To determine if variability of test scores differs between male and female students. To determine if test scores depend on homework scores and gender. To determine if mean test scores differ between the four sections. To determine if test scores are normally distributed.

To determine if mean test scores differ between the four sections.

Which of the following is an example of a chi-square test for independence? Multiple Choice To determine whether there is a relationship between advertising expenditure and sales volume. To determine whether there is a change in media literacy after the training program. To determine whether there is a decrease in lung cancer after the smoking cessation program. To determine whether the likelihood of college admission depends on the race of the applicants.

To determine whether the likelihood of college admission depends on the race of the applicants.

Unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression ________. Multiple Choice can be greater than 1 measures the percentage of variation explained by the regression line indicates whether the slope of the regression line is positive or negative is a proportion

indicates whether the slope of the regression line is positive or negative

A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and so collects monthly data for 25 firms. He estimates the model: Sales = β0 + β1 Advertising + ε. The following table shows a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 40.10 14.08 2.848 0.0052 Advertising 2.88 1.52 −1.895 0.0608 When testing whether Advertising is significant at the 10% significance level, the conclusion is to ________. Multiple Choice reject H0; we can conclude advertising is significant not reject H0; we cannot conclude advertising is significant reject H0; we cannot conclude advertising is significant not reject H0; we can conclude advertising is significant

reject H0; we can conclude advertising is significant

Tiffany & Company has been the world's premier jeweler since 1837. The performance of Tiffany's stock is likely to be strongly influenced by the economy. Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60). The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. Coefficients Standard Error t-stat p-value Lower 95% Upper 95% Intercept 0.0198 0.010 1.98 0.0598 −0.0008 0.0405 RM − Rf 1.827 0.191 9.58 1.494E-13 1.4456 2.2094 When testing whether the beta coefficient is significantly greater than one, the relevant critical value at the 5% significance level is t0.05,58 = 1.672. The conclusion to the test is to ________. Multiple Choice reject H0; we can conclude that the return on Tiffany stock is riskier than the return on the market not reject H0; we can conclude that the return on Tiffany stock is riskier than the return on the market reject H0; we cannot conclude that the return on Tiffany stock is riskier than the return on the market not reject H0; we cannot conclude that the return on Tiffany stock is riskier than the return on the market

reject H0; we can conclude that the return on Tiffany stock is riskier than the return on the market

The standard error of the estimate measures ________. Multiple Choice the standard deviation of the random error the standard deviation of the response variable the standard deviation of the explanatory variable the standard deviation of the correlation coefficient

the standard deviation of the random error