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business
intro stats

Questions and Answers of Intro Stats

Better model? Joe wants to impress his boss. He builds a regression model to predict sales that has 20 predictors and an R2 of 80%. Sally builds a competing model with only 5 predictors, but an R2 of
Significant coefficient? In a regression to predict compensation of employees in a large firm, the predictors in the regression were Years with the firm, Age, and Years of Experience. The coefficient
Residual, leverage, influence, 2 For each of the following cases, would your primary concern about them be that they had a large residual, large leverage, or likely large influence on the regression
Residual, leverage, influence For each of the following cases, would your primary concern about them be that they had a large residual, large leverage, or likely large influence on the regression
More indicators For each of these potential predictor variables say whether they should be represented in a regression model by indicator variables. If so, then suggest what specific indicators
Indicators For each of these potential predictor variables say whether they should be represented in a regression model by indicator variables. If so, then suggest what specific indicators should be
As a class project, students in a large Statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties.These are not a random sample, but
Cramming Students in two basic Spanish classes were required to learn 50 new vocabulary words. One group of 45 students received the list on Monday and studied the words all week. Statistics
Weight loss A weight loss clinic advertises that its program of diet and exercise will allow clients to lose 10 pounds in one month. A local reporter investigating weight reduction gets permission to
Weight and athletics Using the same survey as in Exercise 27, the student examined the relationship between Athletic Participation and Weight. Here are the boxplots of Weight by Athletic
TV and athletics Using a simple random sample, a student asked 200 students questions about their study and workout habits, and received 124 responses. One of the questions asked, “Do you
LA rainfall 2012 The Los Angeles Almanac website reports recent annual rainfall (in inches), as shown in the table.a) Create a 90% confidence interval for the mean annual rainfall in LA.b) If you
Javelin Brianna, a member of the track team, runs an experiment to test how different factors affect her javelin throw. She wants to know if the more expensive(premium) javelin is worth the extra
Video pinball A student runs an experiment to test how different factors affect his score while playing video pinball. Here are the results of 16 runs of an experiment performed in random order.
Pesticides A study published in the journal Environmental Health Perspectives examined the sex ratios of children born to workers exposed to dioxin in Russian pesticide factories. The data covered
Learning math Developers of a new math curriculum called “Accelerated Math” compared performances of students taught by their system with control groups of students in the same schools who were
NY Marathon The New York Times reported the results of the 2003 NY Marathon by listing time brackets and the number of racers who finished within that bracket.Because the brackets are of different
Typing again Nick (see Exercise 19) designed a follow-up experiment to see if having Music or Television on would affect his typing speed. In particular, he’d like to know if he can type just as
Typing For a class project, Nick M. designed and carried out an experiment to see if the room Temperature and the wearing of Gloves affected his typing speed. He ran each combination of hot and cold
Births The National Vital Statistics Report provides information on live Births (per 1000 women), according to the age of the woman (in 5-year brackets—Age used here is the midpoint of the bracket)
Teen traffic deaths 2007 The Insurance Institute for Highway Safety publishes data on a variety of trafficrelated risks. One report gives the numbers of male and female teenagers killed in highway
Is Old Faithful getting older? The data on Old Faithful eruptions that we saw in Review VI Exercise 42 includes another variable recording the Day on which the eruption occurred (where 1 is the first
Study habits The survey in Exercise 14 also asked students about the number of hours they studied. Those doing the survey wanted to know if the average amount of studying varied by sex or by class of
Sleep Using a simple random sample, a student group asked 450 students about their sleep and study habits and received about 200 responses. The group wanted to know if the average amount of sleep
Barbershop music At a barbershop music singing competition, choruses are judged on three scales:Music (quality of the arrangement, etc.), Performance, and Singing. The scales are supposed to be
Nuclear plants Here are data on 32 light water nuclear power plants. The variables are:Cost: In $100,000, adjusted to 1976 base.Date: Date that construction permit was issued in years after 1900.
Paper planes In preparation for a regional paper airplane competition, a student tried out her latest design. The distances her plane traveled (in feet) in 11 trial flights are given here. (The world
Resume fraud In 2002 the Veritas Software company found out that its chief financial officer did not actually have the MBA he had listed on his resume. They fired him, and the value of the
Video racing A student runs an experiment to test how different factors affect his reaction time while playing video games. He uses a specified race course with random hazards and times how long it
Bowling A student runs an experiment to test how different factors affect her bowling performance. She uses 3 levels for the weight of the ball (low, medium, and high) and 2 approaches (standing and
Lost baggage The Bureau of Transportation Statistics of the U.S. Department of Transportation reports statistics about airline performance. For 2005 they report the following number of bags lost per
North and hard The data on water hardness and mortality considered in Part VI Review Exercise 29 also included information on whether the town was north or south of Derby.When that information is
Horses again, a bit less wild In an attempt to control the growth of the herds of wild horses discussed in Review VI Exercise 31, managers sterilized some of the stallions. The variable Sterilized is
Golf A student runs an experiment to test four different clubs on her putting accuracy, recording the distance in centimeters from a small target that she places on the green. She randomizes the club
Football A student runs an experiment to test four different grips on his football throwing distance, recording the distance in yards that he can throw the football using each grip. He randomizes the
Polling How accurate are pollsters in predicting the outcomes of Congressional elections? The table shows the actual number of Democrat seats in the House of Representatives and the number predicted
Mutual funds 2013 We have a sample of mutual funds of various types that report their return (%) in the previous year and in the previous 3 years.a) Create a 95% confidence interval for the
Burger King Recall the Burger King Items menu data from Chapter 7. BK’s nutrition sheet lists many variables.Here’s a multiple regression to predict calories for Burger King foods from Protein
Breakfast cereals again We saw in Chapter 7 that the calorie count of a breakfast cereal is linearly associated with its sugar content. Can we predict the calories of a serving from its vitamin and
Fifty states 2009 Here is a data set on various measures of the 50 United States. The Murder rate is per 100,000, HS Graduation rate is in %, Income is per capita income in dollars, Illiteracy rate
Grades The following table shows the five scores from an Introductory Statistics course. Find a model for final exam score by trying all possible models with two predictor variables. Which model
Body fat one more time Chest size might be a good predictor of body fat. Here’s a scatterplot of %Body Fat vs. Chest Size.A regression of %Body Fat on Chest Size gives the following equation:a) Is
Breakfast cereals We saw in Chapter 7 that the calorie content of a breakfast cereal is linearly associated with its sugar content. Is that the whole story? Here’s the output of a regression model
Body fat revisited The data set on body fat contains 15 body measurements on 250 men from 22 to 81 years old. Is average %Body Fat related to Weight? Here’s a scatterplot:And here’s the simple
GPA and SATs A large section of Stat 101 was asked to fill out a survey on grade point average and SAT scores.A regression was run to find out how well Math and Verbal SAT scores could predict
Admin performance The AFL-CIO has undertaken a study of the yearly salaries (in thousands of dollars) of 30 administrative assistants. The organization wants to predict salaries from several other
Home prices II Here are some diagnostic plots for the home prices data from Exercise 15. These were generated by a computer package and may look different from the plots generated by the packages you
Predicting finals II Here are some diagnostic plots for the final exam data from Exercise 13. These were generated by a computer package and may look different from the plots generated by the
More hill races 2008 Here is the regression for thewomen’s records for the same Scottish hill races we considered in Exercise 14:a) Compare the regression model for the women’s records with that
Home prices Many variables have an impact on determining the price of a house. A few of these are Size of the house (square feet), Lotsize, and number of Bathrooms.Information for a random sample of
Scottish hill races 2008 Hill running—races up and down hills—has a written history in Scotland dating back to the year 1040. Races are held throughout the year at different locations around
Predicting final exams How well do exams given during the semester predict performance on the final?One class had three tests during the semester. Computer output of the regression givesa) Write the
More interpretations A household appliance manufacturer wants to analyze the relationship between total sales and the company’s three primary means of advertising(television, magazines, and radio).
Interpretations A regression performed to predict the selling price of houses found the equation Price = 169,328 + 35.3 Area + 0.718 Lotsize - 6543 Age where Price is in dollars, Area is in square
Movie output Here is another part of the regression output for the movies in Exercise 3:Source Sum of Squares df Mean Square F-ratio Regression 224995 3 74998.4 34.8 Residual 249799 116 2153.44a)
Movie R-squared In the regression model of Exercise 3,a) What is the R2 for this regression? What does it mean?b) Why is the “Adjusted R Square” in the table different from the “R Square”?
More movie testsa) What is the null hypothesis tested for the coefficient of Run Time in the regression of Exercise 3?b) What is the t-statistic corresponding to this test?c) Why is this t-statistic
Movie tests In the regression output for the movies of Exercise 3,a) What is the null hypothesis tested for the coefficient of Stars in this table?b) What is the t-statistic corresponding to this
Movie residuals For the movies regression, here is a histogram of the residuals. What does it tell us about these Assumptions and Conditions?a) Linearity conditionb) Nearly Normal conditionc) Equal
More movies For the movies examined in Exercise 4, here is a scatterplot of USGross vs. Budget:What (if anything) does this scatterplot tell us about the following Assumptions and Conditions for the
Movie profits again A middle manager at an entertainment company, upon seeing the analysis of Exercise 3, concludes that longer movies make less money. He argues that his company’s films should all
Movie profits What can predict how much a motion picture will make? We have data on a number of recent releases that includes the USGross (in $M), the Budget($M), the Run Time (minutes), and the
Candy sales A candy maker surveyed chocolate bars available in a local supermarket and found the following least squares regression model:Calories = 28.7 + 11.98Fat1g2 + 3.76Sugar1g2.a) The
House prices The following regression model was found for houses in an area of upstate New York:Price = 20,668.96 - 7753.05Bedrooms + 113.74Living Area.a) Find the predicted price of a 3 bedroom,
As a class project, students in a large Statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties.These are not a random sample, but
Containers one more time Another student performs a one-way ANOVA on the container data of Exercise 20, using the 4 treatments water room, water outside, coffee room, and coffee outside. Perform this
Batteries once more Another student analyzed the battery data from Exercise 25, using a one-way ANOVA.He considered the experimental factor to be an 8-level factor consisting of the 8 possible
Peas In an experiment on growing sweet peas, a team of students selected 2 factors at 4 levels each and recorded Weight, Stem Length, and Root Length after 6 12 days of growth. They grew plants using
Batteries A student experiment was run to test the performance of 4 brands of batteries under 2 different Environments (room temperature and cold). For each of the 8 treatments, 2 batteries of a
Chromatography again Refer back to the experiment in Exercise 22. Instead of Total counts, redo the analysis using log(Total counts) as the response. Do your conclusions change? How? Are the
Gas additives again Refer back to the experiment in Exercise 21. Instead of mpg redo the analysis using log(mpg) as the response. Do your conclusions change?How? Are the assumptions of the model
Chromatography A gas chromatograph is an instrument that measures the amounts of various compounds contained in a sample by separating the various constituents.Because different components are
Gas additives An experiment to test a new gasoline additive, Gasplus, was performed on three different cars: a sports car, a minivan, and a hybrid. Each car was tested with both Gasplus and regular
Containers revisited Building on the cup experiment of the Chapter 4 Step-By-Step, a student selects one type of container and designs an experiment to see whether the type of Liquid stored and the
Sprouts again The students running the sprouts experiment(Exercise 12) also kept track of the number of beans sprouted (out of 40) for each of the 36 dishes. Here are the partial boxplots of Sprouts
Washing For his final project, Jonathan examined the effects of two factors on how well stains are removed when washing clothes. On each of 16 new white handkerchiefs, he spread a teaspoon of dirty
Basketball shots A student performed an experiment to see if her favorite sneakers and the time of day might affect her free throw percentage. She tried shooting with and without her favorite
Fish and prostate Refer back to Exercise 14. Perform your own analysis of the data to see if eating fish and contracting prostate cancer are related.
Baldness and heart disease again Refer back to Exercise 13. Perform your own analysis of the data to see if baldness and heart disease are related. Do your conclusions support the claim that baldness
Fish and prostate The Chapter 3 Step-By-Step looked at a Swedish study that asked 6272 men how much fish they ate and whether or not they had prostate cancer.Here are the data:Armed with the methods
Baldness and heart disease A retrospective study examined the link between baldness and the incidence of heart disease. In the study, 1435 middle-aged men were selected at random and examined to see
Sprouts An experiment on mung beans was performed to investigate the environmental effects of salinity and water temperature on sprouting. Forty beans were randomly allocated to each of 36 petri
Crash analysis The National Highway Transportation Safety Administration runs crash tests in which stock automobiles are crashed into a wall at 35 mph with dummies in both the passenger and the
Gas mileage again Refer to the experiment in Exercise 8.After analyzing his data the student reports that the F-ratio for Tire Pressure is 4.29 with a P-value of 0.030, the F-ratio for Acceleration
Popcorn again Refer to the experiment in Exercise 7.After collecting her data and analyzing the results, the student reports that the F-ratio for Power is 13.56 and the F-ratio for Time is 9.36.a)
Gas mileage revisited In Chapter 26 we saw a student’s experiment to study the effect of Tire Pressure and Acceleration on gas mileage. He devises a system so that his Jeep Wagoneer uses gasoline
Popcorn revisited In the previous chapter we saw a two-factor experiment to test how microwave power and temperature affect popping. She chooses 3 levels of Power (low, medium, and high) and 3 Times
Have ANOVA cookie Here is the ANOVA table for the cookie experiment of Exercise 2 along with an interaction plot. What does the interaction term say about the cookie recipes? Analysis of Variance For
Student TV interactions Here is an ANOVA table with an interaction term and the corresponding interaction plot for the TV watching data of Exercise 1. What does the interaction term mean here?
Cookie assumptions The student performing the chocolate chip cookie experiment of Exercise 2 planned to analyze his results with an Analysis of Variance on two factors. Here are some displays. Do you
Student TV assumptions The TV watching study of Exercise 1 was collected as a survey of students at a small college. Do the assumptions of ANOVA appear to be met? Here are some displays to help in
Cookies A student performed an experiment to compare chocolate chip cookie recipes. He baked batches of cookies with different amounts of Sugar: 0.5, 0.375, and 0.25 cups, and with different kinds of
Students set up an experiment to investigate factors that determine how far a paper airplane will fly. Among the factors are whether the plane is constructed of copier paper or heavier construction
Analgesics A pharmaceutical company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment, 27 volunteers were selected and 9 were randomly assigned
Downloading To see how much of a difference time of day made on the speed at which he could download files, a college sophomore performed an experiment. He placed a file on a remote server and then
Cereals, redux We also have data on the protein content of the cereals in Exercise 19 by their shelf number. Here are the boxplot and ANOVA table:a) What are the null and alternative hypotheses?b)
Cereals once more We first saw data on breakfast cereals in Chapter 7. Supermarkets often place similar types of cereal on the same supermarket shelf. We have data on the shelf as well as the sugar,
Fertilizers A biology student is studying the effect of 10 different fertilizers on the growth of mung bean sprouts.She sprouts 12 beans in each of 10 different petri dishes, and adds the same amount
School system A school district superintendent wants to test a new method of teaching arithmetic in the fourth grade at his 15 schools. He plans to select 8 students from each school to take part in
Auto noise filters In a statement to a Senate Public Works Committee, a senior executive of Texaco, Inc., cited a study on the effectiveness of auto filters on reducing noise.Because of concerns

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