BNAL Final

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A candy bar manufacturer is interested in trying to estimate how sales are influenced by price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below River Falls $1.30 100 Hudson $1.60 90 Ellsworth $1.80 90 Prescott $2.00 40 Rock Elm $2.40 38 Stillwater $2.90 32 Referring to table 13-2, what is the coefficient of correlation for these data?

-0.8854

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. Referring to Table 10-1, what is the value of the test statistic?

-11.8092

A candy bar manufacturer is interested in trying to estimate how sales are influenced by price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below River Falls $1.30 100 Hudson $1.60 90 Ellsworth $1.80 90 Prescott $2.00 40 Rock Elm $2.40 38 Stillwater $2.90 32 Referring to Table 13-2, what is the estimated mean change in the sales of the candy bar if price goes up by $1.00?

-48.193

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 Referring to Table 14-3, to test for the significance of the coefficient on gross domestic product, the p-value is

0.0001

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?

0.0780

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: where Y = demand (in thousands) and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis is shown below: what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?

0.3647

A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information: E Y X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 Referring to Table 14-2, for these data, what is the estimated coefficient for the number of economics courses taken, b2?

0.616

0.8330

1.054

A computer used by a 24-hour banking service is supposed to randomly assign each tansaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors Memory Location 1 2 3 4 5 Number of Reported Errors 11 12 6 9 10 Number of Correct Transactions 71 88 68 83 92 The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. Referring to Table 12-4, the calculated value of the test statistic is

1.500

A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information: E Y X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 Referring to Table 14-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate?

12.20

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 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 output: Referring to Table 11-1, the within groups of degrees of freedom is

The following Excel Table are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course. Referring to Table 13-6, which of the following statements is true?

2% of the total variability in score received can be explained by percentage attendance.

A professor of industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information: E Y X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 Referring to Table 14-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate?

24.87

The following table contains the number of complaints received in a department store for the first 6 months of last year Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 If this series is smoothed using exponential smoothing with a smoothing constant of 1/3, what would be the first term?

6.932

A candy bar manufacturer is interested in trying to estimate how sales are influenced by price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below River Falls $1.30 100 Hudson $1.60 90 Ellsworth $1.80 90 Prescott $2.00 40 Rock Elm $2.40 38 Stillwater $2.90 32 Referring to Table 13-2, if the price of the candy bar is set at $2, the estimated mean sales will be

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 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 output: Refering to Table 11-1, the among group (between-group) mean squares is

70.8

The following table contains the number of complaints received in a department store for the first 6 months of last year Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 If a three-term moving average is used to smooth this series, what would be the second calculated term?

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education in years. The builder randomly selected 50 families and ran the multiple regression. Excel output is provided below Referring to Table 14-4, what fraction of the variablility in house size is explained by income, size of family, and education?

74.8%

A computer software devleoper would like to use the number of downloads (in thousands) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot from a data set of 30 different sharewares that he has developed. Referring to table 13-11, which of the following is the correct interpretation for the coefficient of determination?

75.54% of the variation in revenue can be explained by the variation in the number of dowloads.

A candy bar manufacturer is interested in trying to estimate how sales are influenced by price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below River Falls $1.30 100 Hudson $1.60 90 Ellsworth $1.80 90 Prescott $2.00 40 Rock Elm $2.40 38 Stillwater $2.90 32 Referring to Table 13-2, what is the percentage of the total variation in candy bar sales explained by the regression model?

78.39%

Recent studies have found that American children are more obese that in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten year olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% of significance. Referring to Table 12-13, If there is no connection between weights and average numbers of hours spent watching TV, we should expect how many children to be spending more than 6 hours on average watching TV and are more than 10 lbs. underweight?

The following table contains the number of complaints received in a department store for the first 6 months of last year Month Complaints January 36 February 45 March 81 April 90 May 108 June 144 Suppose the last two smoothed values are 81 and 96 (Note: they are not) what would you forecast as the value of the time series for July?

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: where Y = demand (in thousands) and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis is shown below: What is the correct interpretation of the coefficient of multiple determination?

98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price

in what type of test is the variable of interest difference between the values of the observations rather than the observations themselves?

A test for the difference between the means of 2 related populations

Many factors determine the attendance at Major League Baseball games. These factors can include when the game is played, the weather, the opponent, whether or not the team is having a good season, and whether or not a marketing promotion is held. Data from 80 games of the Kansas City Royals for the following variables are collected. ATTENDANCE = Paid attendance for the game TEMP = High temperature for the day WIN% = Team's winning percentage at the time of the game OPWIN% = Opponent team's winning percentage at the time of the game WEEKEND − 1 if game played on Friday, Saturday or Sunday; 0 otherwise PROMOTION − 1 = if a promotion was held; 0 = if no promotion was held The regression results using attendance as the dependent variable and the remaining five variables as the independent variables are presented below The coefficient of multiple determination of each of the 5 predictors with all the other remaining predictors are respectively, 0.2675, 0.3101, 0.1038, 0.7325, and 0.7308. What is the correct interpretation for the estimated coefficient for TEMP?

As the high temperature increases by one degree, the estimated mean paid attendance will increase by 51.70 taking into consideration all the other independent variables included in the model.

If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is

Both the Z test and the X2 Test

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. she proceeds to randomly select 26 large corporations and record information in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending . What should the microeconomist who developed this multiple regression model be particularly concerned with?

Collinearity

The owner of a local night club has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not , no entertainment changes will be made. suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to havae a level of significance at 0.02, what decision should she make?

Do no reject H0

A statistics professor wanted to test whether the grade on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples

False

A test for whether one proportion is higher than the other can be performed using the chi-square distribution

False

Each forecast using the method of weighted average smoothing depends on all the previous observations in the time series

False

If you are comparing the mean sales among 3 different brands you are dealing with a three-way ANOVA design.

False

In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

False

The larger the p-value, the more likely you are to reject the null hypothesis

False

The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions

False

True or False: Collinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables

False

True or False: In stepwise regression, an independent variable is not allowed to be removed from the model once it has entered into the model

False

True or False: So that we can fit curves as well as lines by regression, we often use mathematical manipulations for converting one variable into a different form. These manipulations are called dummy variables

False

True or False: The stepwise regression approach takes into consideration all possible models.

False

suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

False

the sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations

False

For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $3.7297 thousands.

A real estate company is interested in testing whether the mean team that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes Reffering to table 10-3, which of the following represents the relevant hypotheses tested by the real estate company?

H) uG - uM >= Vs. uG-uM < 0

the owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. she would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:

H0 u =<30 vs H1: u > 30

A computer software devleoper would like to use the number of downloads (in thousands) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot from a data set of 30 different sharewares that he has developed. Referring to table 13-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?

H0: B1 = 0

H0: u j = 0 Vs. H1: u A - u j = 0

In testing for differences between the means of two independent populations, the null hypothesis is

H0: u1-u2 = 0

In testing for differences between the means of two related populations, the null hypothesis is

H0: uD = 0.

The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was:"Do you think sexual harassment is a major problem in the American workplace?" 24% of the men compared to 62% of the women responded "Yes". Assuming W designates women's responses and M designates men's, what hypothesis should The Wall Street Journal test in order to show that is claim is true?

H0:πW - πM =< 0 Vs. H1: πW - πM > 0

To explain personal consumption (CONS) measured in dollars, data is collected for > A regression analysis was performed with CONS as the dependent variable and ln(CRDTLIM), ln(APR), ln(ADVT), and GENDER as the independent variables. The estimated model was Y = 2.28 - 0.29 1n(CRDTLIM) + 5.77 1n(APR) + 2.35 In(ADVT) + 0.39 GENDER, with 0 being used as an index for males and 1 as an index for females. what is the correct interpretation for the estimated coefficient for GENDER?

Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be $0.39 higher than males.

If attendance increases by 1%, the estimated mean score received will increase by 0.241 percentage points.

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education in years. The builder randomly selected 50 families and ran the multiple regression. Excel output is provided below Referring to Table 14-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model?

Income is significant in explaining house size and should be included in the model because its p-value is less that 0.01.

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education in years. The builder randomly selected 50 families and ran the multiple regression. Excel output is provided below Referring to Table 14-4, which of the independent variables in model are significant at the 5% level?

Income, Size

The effect of an unpredictable, rare event will be contained in the _______ component.

Irregular

Which of the following is not an advantage of exponential smoothing?

It enables us to perform more than one-period ahead forecasting

Which of the following statements about moving averages is not true?

It gives greater weight to more recent data

The F test statistic in a one-way ANOVA is

MSA/MSW

In selecting an appropriate forecasting model, the following approaches are suggested

Measure the size of the forecasting error Use the principle of the parsimony Perform a residual analysis (All of the above)

An airline wants to select a computer software package for its reservation system. Four software packages (1,2,3,&4) are commercially available. The airline will choose the package that bumps the fewest mean number of passengers 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 given below. How should the data be analyzed? Package 1: 12, 14, 9, 11, 16 Package 2: 2, 4, 7, 3, 1 Package 3: 10, 9, 6, 10, 12 Package 4: 7, 6, 6, 15, 12

One-way ANOVA F test

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Towards Life, which measures motivation for upward mobility. The SSATL scores are summarized below. Refeerring to Table 10-1, Judging from the way the data were collected, which test would likely be most appropriate to employ?

Pooled-variance t test for the difference between two means

One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X!) the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Excel outputs of two regression models. Referring to Table 14-6, what is your decision and conclusion for the test H 0: B2 = 0 vs H 1: B2 < 0 at the a = 0.01 level of significance using Model 1?

Reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs.

The owner of a local nightclub has recently surveyed a random sample of n = 250 customer of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample SD was 5 years. If she wants to have a level of significance at 0.01 what conclusion can she make?

There is not sufficient eveidence that the mean age of her customers is greater than 30.

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 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 output: Reffering to table 11-1, at a significance level of 1%

There is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same.

When would you use the Tukey-Kramer procedure?

To test for differences in pairs of means

A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each two tests: one given after two hours' sleep and one after eight hours' sleep. The test the researcher should use would be a related samples test.

True

In a one-factor ANOVA analysis, the among sum of squares and within sum of square must add up to the total sum of square.

True

In selecting a forecasting model, we should perform a residual analysis

True

Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.043. The null hypothesesis should be rejected if the chosen level of significance is 0.05.

True

The Chancellor of a university has commissioned a team to collect data on students' GPAs and the amount of time they spend bar hopping every week (Measure in Minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs. His team should use a t test on the slope of the popular regression

True

The director of admissions at a state college is interested in seeing if admissions status (admitted waiting list, denied admission at his college is independent of the type of community in which an applicant resides He take a sample of recent admissions decisions and forms the following table He will use the table to do a Chi-square test with a level of significance of 0.01 Referrring to Table 12-11, the alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides"

True

The smaller the p-value, the stronger the evidence is against the null hypothesis

True

The statement of the null hypothesis always contains an equality

True

True or False: The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity

True

True or False: the principle of parsimony indicates that the simplest model that gets the job done adequately should be used

True

Recent studies have found that American children are more obese that in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten year olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% of significance. Referring to Table 12-13, suppose the value of the test statistic was 30.00 (which is not the correct value) and the critical value at 1% level of significance was 10.00 (which is not the correct value), which of the following conclusions would be correct?

We will reject the mull and conclude that mean number of hours spent watching TV and weights are not independent.

X2 test for difference among more than two proportions.

Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table. The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment?

Z test for difference between tow proportions

if an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000

a one-tail test should be utilized.

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000

a two-tail test should be utilized.

The strength of the linear relationship between two numerical variables may be measured by the

coefficient of correlation

One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X!) the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Excel outputs of two regression models. Referring to Table 14-6, the estimated value of the partial regression parameter B1 in Model 1 means that

holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51

In a simple linear regression problem, r and b1

must have the same sign.

A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented ( all of these might not be necessary to answer the questions which follow.) The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Referring to Table 10-7, the test to perform is a

paired t test for the mean difference

The t test for the difference between the means of 2 independent populations assumes that the repective

populations are approximately normal

The Y-intercept (b0) represents the

predicted value when X = 0

In a one-way ANOVA, if the computed F-statistic is greater than the critical F value you may

reject H0 since there is evidence that not all the means are the same

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. Reffering to Table 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test.

smaller that 0.01

In multiple regression, the ________ procedure permits variables to enter and leave the model at different stages of its development

stepwise regression

A ____ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis

test statistic

A regression diagonostic tool used to study the possible effects of collinearity is

the VIF

When using the exponentially weighted moving averages for purposes of forecasting rather than smoothing

the current smoothed value becomes the forecast

The residual represents

the difference between the actual Y values and the predicted Y values

the slope (b1) represents

the estimated average change in Y per unit change in X.

In a multiple regression problem involving two independent cariables, if b1 is computed to be +2.0, it means that

the estimated mean of Y increases by 2 units for each increas of 1 unit of x1, holding x2 constant.

If the p-value is less than a in a two-tail test,

the null hypothesis should be rejected

a dummy variable is used as an independent variable when

the variable involved is categorical

there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same

In a one-way ANOVA, the null hypothesis is always

there is no difference in the population means.

The method of moving averages is used

to smooth a series

The overall upward or downward pattern of the data in annual time series will be contained in the _______ component.

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