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statistics alive

Questions and Answers of Statistics Alive

12.99 Multiple choice: Income and height University of Rochester economist Steven Landsburg surveyed economic studies in England and the United States that showed a positive correlation between
12.98 Multiple choice: Regress x on y The regression of y on x has a prediction equation of yn = -2.0 + 5.0x and a correlation of 0.3. Then, the regression of x on ya. also has a correlation of
12.97 Multiple choice: Slope and correlation The slope of the least squares regression equation and the correlation are similar in the sense thata. They both must fall between -1 and +1.b. They both
12.96 Multiple choice: Correlation invalid The correlation is appropriate for describing association between two quantitative variablesa. Even when different people measure the variables using
12.95 Multiple choice: Interpret r One can interpret r = 0.30 or the corresponding r2 = 0.09 as follows:a. A 30% reduction in error occurs in using x to predict y.b. A 9% reduction in error occurs in
12.94 Population growth Exercise 12.57 about U.S. population growth showed a predicted growth rate of 13% per decade.a. Show that this is equivalent to a 1.23% predicted growth per year.b. Explain
12.93 Decrease in home values A Freddie Mac quarterly statement(May 2010) reported that U.S. home sales for one of the central regions (including Illinois, Indiana, Ohio, and Wisconsin) have shown
12.92 Lots of standard deviations Explain carefully the interpretations of the standard deviations (a) sy, (b) sx, (c) residual standard deviation s, and (d) se of slope estimate b.
12.91 Assumptions fail? Refer to the previous exercise. In view of these assumptions, indicate why such a model would or would not be good in the following situations:a. x = year (from 1900 to 2005),
12.90 Assumptions What assumptions are needed to use the linear regression model to (a) obtain a meaningful fit that represents the true relationship well and (b) to make inferences about the
12.89 df for t tests in regression In regression modeling, for t tests about regression parameters, df = n - number of parameters in equation for the mean.a. Explain why df = n - 2 for the model my =
12.88 All models are wrong The statistician George Box, who had an illustrious academic career at the University of Wisconsin, is often quoted as saying, “All models are wrong, but some models are
12.87 Dollars and pounds Annual income, in dollars, was the response variable in a regression analysis. For a British version of a written report about the analysis, all responses were converted to
12.86 Mileage and weight Explain why the correlation between x = weight of a car and y = mileage of a car is likely to be smaller if we use a random sample of sports cars than if we use a random
12.85 Height and weight Suppose the correlation between height and weight is 0.50 for a sample of males in elementary school and 0.50 for a sample of males in middle school.If we combine the samples,
12.84 Regression toward the mean paradox Does regression toward the mean imply that, over many generations, there are fewer and fewer very short people and very tall people? Explain your reasoning.
12.83 Sports and regression One of your relatives is a big sports fan but has never taken a statistics course. Explain how you could describe the concept of regression toward the mean in terms of a
12.82 Iraq war and reading newspapers A study by the Readership Institute3 at Northwestern University used survey data to analyze how newspaper reader behavior was influenced by the Iraq war. The
12.81 Football point spreads For a football game in the National Football League, let y = difference between number of points scored by the home team and the away team (so, y 7 0 if the home team
12.80 Female athletes’ speed For the High School Female Athletes data set on the book’s website, conduct a regression analysis using the time for the 40-yard dash as the response variable and
12.79 GPA and TV watching Using software with the FL Student Survey data file on the book’s website, conduct regression analyses relating y = high school GPA and x = hours of TV watching. Prepare a
12.78 Runs and hits Refer to the previous exercise. Conduct a regression analysis of y = RUNS and x = HIT. Does a straight-line regression model seem appropriate? Prepare a reporta. Using graphical
12.77 Softball data The Softball data file on the book’s website contains the records of a University of Georgia coed intramural softball team for 277 games over a 20-year period. (The players
12.76 Match the scatterplot Match each of the following scatterplots to the description of its regression and correlation.The plots are the same except for a single point.Justify your answer for each
12.75 World population growth The table shows the world population size (in billions) since 1900.a. Let x denote the number of years since 1900. The exponential regression model fitted to y =
12.74 Florida population The population size of Florida(in thousands) since 1830 has followed approximately the exponential regression yn = 4611.0362x. Here, x = year - 1830 (so, x = 0 for 1830 and x
12.73 Savings growth You invest €2000 in an account having an interest rate such that your principal doubles every 10 years.a. How much money would you have after 60 years?b. If you were still
12.72 Leg press ANOVA The analysis in the previous exercise has the ANOVA table shown.a. For those female athletes who had maximum bench press equal to the sample mean of 80 pounds, what is the
12.71 Bench press predicting leg press For the study of high school female athletes, when we use x = maximum bench press (maxBP) to predict y = maximum leg press (maxLP), we get the results that
12.70 Exercise and college GPA For the Georgia Student Survey file on the book’s website, let y = exercise and x = college GPA.a. Construct a scatterplot. Identify an outlier that could influence
12.69 Types of variability Refer to the previous two exercises.a. Explain the difference between the residual standard deviation of 52,771.5 and the standard deviation of 56,357 reported for the
12.68 Bedrooms affect price? Refer to the previous exercise.a. Explain what the regression parameter b means in this context.b. Construct and interpret a 95% confidence interval for b.c. Use the
12.67 Bedroom residuals For the House Selling Prices FL data set on the book’s website, when we regress y = selling price (in dollars) on x = number of bedrooms, we get the results shown in the
12.66 Income and education in Florida The FL Crime data file on the book’s website contains data for all counties in Florida on y = median annual income (thousands of dollars)for residents of the
12.65 Tall people Do very tall parents tend to have children who are even taller, or tall but not as tall as they are?Explain, identifying the response and explanatory variables and the role of
12.64 Stem cells In the article, “Variation in cancer risk among tissues can be explained by the number of stem cell divisions” (Tomasetti and Vogelstein, Science, vol.47, 2015), the authors
12.63 Theory exam–practical exam correlation A report summarizing scores for students appearing in a theory examination x and a practical examination y states that x = 270, y = 360, sx = 60, sy =
12.62 Academic performance and participation in extracurricular activities Let y = grade point average (GPA) and x =number of times a student has participated in extracurricular activities, measured
12.61 More leaf litter Refer to the previous exercise.a. The correlation equals -0.890 between x and y and-0.997 between x and log(y). What does this tell you about which model is more appropriate?b.
12.60 Leaf litter decay Ecologists believe that organic material decays over time according to an exponential decay model.This is the case 0 6 b 6 1 in the exponential regression model, for which my
12.59 Age and death rate Let x denote a person’s age and let y be the death rate, measured as the number of deaths per thousand individuals of a fixed age within a period of a year. For women in a
12.58 Future shock Refer to the previous exercise, for which predicted population growth was 14.18% per decade.Suppose the growth rate is now 15% per decade. Explain why the population size will (a)
12.57 U.S. population growth The table shows the approximate U.S. population size (in millions) at 10-year intervals beginning in 1900. Let x denote the number of decades since 1900. That is, 1900 is
12.56 Moore’s law today The following data show the number of components (per square inch, in millions) being packed on a Pentium-type chip, for years 1994 to 2015.Let x be the number of years
12.55 Growth by year versus decade It is expected that the female population in a city will double in two decades.a. Explain why this is possible for a growth rate of 3.6% a year. (Hint: What does
12.54 Savings grow exponentially You invest $100 in a savings account with interest compounded annually at 10%.a. How much money does the account have after one year?b. How much money does the
12.53 Cell phone ANOVA Report the ANOVA table for the previous exercise.a. Verify that total SS = residual SS + regression SS. Explain what each of the three sums of squares represent.b. Find the
12.52 Predicting cell phone weight Refer to the cell phone data file on the book’s website. Regress y = weight on x = capacity of battery, excluding the outlier (phone no. 70).a. Stating the
12.51 Understanding an ANOVA table For a random sample of Indian states, the ANOVA table shown refers to hypothetical data on x = tax revenue in Indian rupees and y = agricultural subsidies in Indian
12.50 Assumption violated For prediction intervals, an important inference assumption is a constant standard deviation s of y values at different x values. In practice, the standard deviation often
12.49 Variability and F Refer to the previous two exercises.a. In the ANOVA table, show how the Total SS breaks into two parts and explain what each part represents.b. From the ANOVA table, explain
12.48 Predicting leg press Refer to the previous exercise.MINITAB reports the tabulated results for observations at x = 25.a. Show how MINITAB got the “Fit” of 365.7.b. Using the predicted value
12.47 ANOVA table for leg press Exercise 12.15 referred to an analysis of leg strength for 57 female athletes, with y = maximum leg press and x = number of 200-pound leg presses until fatigue, for
12.46 CI versus PI Using the context of the previous exercise, explain the difference between the purpose of a 95% prediction interval (PI) for an observation and a 95% confidence interval (CI) for
12.45 Predicting annual salary For a random sample of residents from a district in South Carolina, a regression analysis is conducted of y = salary in thousands of dollars and x = years of education.
12.44 Predicting house prices The House Selling Prices FL data file on the book’s website has several predictors of house selling prices. The table here shows the ANOVA table for a regression
12.43 Bench press residuals The figure is a histogram of the standardized residuals for the regression of maximum bench press on number of 60-pound bench presses for the high school female
12.42 Loves TV and exercise For the Georgia Student Survey file on the book’s website, let y = time exercising and x = time watching TV. One student reported watching TV an average of 180 minutes a
12.41 Poor predicted sales The MINITAB output shows the large standardized residuals for studying sales in thousands of pounds as a response using marketing in thousands of pounds as the explanatory
12.40 Correlations for the strong and for the weak Refer to the High School Female Athlete and Male Athlete Strength data files on the book’s website.a. Find the correlation between number of
12.39 Violent crime and single-parent families Use software to analyze the U.S. Statewide Crime data file on the book’s website on y = violent crime rate and x = percentage of single parent
12.38 Yale and UConn For which student body do you think the correlation between high school GPA and college GPA would be higher: Yale University or the University of Connecticut? Explain why.
12.37 Food and drink sales The owner of Bertha’s Restaurant is interested in whether an association exists between the amount spent on food and the amount spent on drinks for the restaurant’s
12.36 Car weight and mileage The Car Weight and Mileage data file on the book’s website shows the weight and the mileage per gallon of gas of 25 cars of various models.The regression of mileage on
12.35 Golf regression In the first round of a golf tournament, five players tied for the lowest round, at 65. The mean score of all players was 75. If the mean score of all players is also 75 in the
12.34 What’s wrong with your stock fund? Last year you looked at all the financial firms that had stock growth funds. You picked the growth fund that had the best performance last year (ranking at
12.33 Was the advertising strategy helpful? Among the 100 different varieties of bread made by a bakery, the marketing manager selected the 10 worst-selling bread types and promoted them through a
12.32 Placebo helps cholesterol? A clinical trial admits subjects suffering from high cholesterol, who are then randomly assigned to take a drug or a placebo for a 12-week study.For the population,
12.31 GPA and study time Refer to the association you investigated in Exercise 12.7 between study time and college GPA. Using software or a calculator with the data file you constructed for that
12.30 GPA and TV watching For the Georgia Student Survey data file on the book’s website, the correlation between daily time spent watching TV and college GPA is -0.35.a. Interpret r and r2. Use
12.29 GRE score regression toward mean Refer to the previous exercise.a. Predict the verbal GRE score for a student whose math GRE score = 170.b. The correlation is 0.8. Interpret the prediction in
12.28 Verbal and math GRE scores All graduate students who attend an Irish university must submit their math and verbal GRE scores. Both the scores have a mean of 150 and a standard deviation of 6.5.
12.27 Body fat For the Male Athlete Strength data file on the book’s website, the correlation between weight (pounds)and percent body fat (BF%) equals 0.883.a. Interpret the sign and the strength
12.26 Sit-ups and the 40-yard dash Is there a relationship between x = how many sit-ups you can do and y = how fast you can run 40 yards (in seconds)? The MINITAB output of a regression analysis
12.25 Sketch scatterplot Sketch a scatterplot, identifying quadrants relative to the sample means as in Figure 12.2, for which (a) the slope and correlation would be negative and (b) the slope and
12.24 When can you compare slopes? Although the slope does not measure association, it is useful for comparing effects for two variables that have the same units. Let x = GDP (thousands of pounds per
12.23 Euros and thousands of euros If a slope is 1.63 when x = investment in thousands of euros, then what is the slope when x = investment in euros? (Hint: A €1 change has only 1/1000 of the
12.22 Battery capacity Refer to the cell phone data set from Exercise 12.9 about various specs of cell phones. Treat the weight of the phone as the response and the capacity of the battery as the
12.21 GPA and skipping class—revisited Refer to the association you investigated in Exercise 12.8 between skipping class and college GPA. Using software with the data file you constructed,
12.20 GPA and study time—revisited Refer to the association you investigated in Exercise 12.7 between study time and college GPA. Using software with the data file you constructed, conduct a
12.19 Investment and rate of interest. A market research company wants to study the relationship between y = investment(in pounds) and x = rate of interest (in percentage), for a British commercial
12.18 CI and two-sided tests correspond Refer to the previous two exercises. Using significance level 0.05, what decision would you make? Explain how that decision is in agreement with whether 0
12.17 More girls are good? Repeat the previous exercise using x = number of daughters the woman had, for which the slope estimate was 0.44 1se = 0.292.
12.16 More boys are bad? A study of 375 women who lived in pre-industrial Finland (by S. Helle et al., Science, vol. 296, p. 1085, 2002), using Finnish church records from 1640 to 1870, found that
12.15 Strength through leg press The high school female athlete strength study also considered prediction of y = maximum leg press (maxLP) using x = number of 200-pound leg presses (LP200). MINITAB
12.14 House prices in bad part of town Refer to the previous exercise. Of the 100 homes, 25 were in a part of town considered less desirable. For a regression analysis using y = selling price and x =
12.13 Confidence interval for slope Refer to the previous exercise, which mentioned a confidence interval of (64, 90)for the slope. The 100 houses included in the data set had sizes ranging from 370
12.12 Predicting house prices For the House Selling Prices FL data file on the book’s website, MINITAB results of a regression analysis are shown for 100 homes relating y = selling price (in
12.11 t-score? A regression analysis is conducted with 32 observations.a. What is the df value for inference about the slope b?b. Which two t test statistic values would give a P-value of 0.10 for
12.10 Exercise and watching TV For the Georgia Student Survey file on the book’s website, let y = exercise and x = watch TV (minutes per day).a. Construct a scatterplot. Identify an outlier that
12.9 Cell phone specs Refer to the cell phone data set available on the book’s website, which shows various specs of a random sample of cell phones. Engineers would like to analyze how the weight
12.8 GPA and skipping class Refer to the previous exercise.Now let x = number of classes skipped and y = college GPA.a. Construct a scatterplot. Does the association seem to be positive or
12.7 Study time and college GPA Exercise 3.39 in Chapter 3 showed data collected at the end of an introductory statistics course to investigate the relationship between x = study time per week
12.6 Fast food and indigestion Let y = number of times fast food was eaten in the past month and x = number of times indigestion happened in the past month, measured for all students at your school.
12.5 Ensuring linear relationship In a linear regression model, how does one ensure that the relationship between the dependent variable and the independent variable is linear? Explain.
12.4 Higher income with experience Suppose the regression line my = -10,000 + 9500x models the relationship for the population of working adults in a country between x = experience (in years) and the
12.3 Predicting maximum bench strength in males For the Male Athlete Strength data file on the book’s website, the prediction equation relating y = maximum bench press(maxBP) in kilograms to x =
12.2 Predicting car mileage Refer to the previous exercise.a. Find the predicted mileage for the Toyota Corolla, which weighs 2,590 pounds.b. Find the residual for the Toyota Corolla, which has
12.1 Car mileage and weight The Car Weight and Mileage data file on the book’s website shows the weight (in pounds) and mileage (miles per gallon) of 25 different model autos.a. Identify the
11.90 Conduct a research study using the GSS Go to the GSS codebook at sda.berkeley.edu/GSS. Your instructor will assign a categorical response variable. Conduct a research study in which you find at

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