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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

A recent survey asked each participant whether he or she believes in heaven and in hell. Of the 1314 participants, a proportion of 0.85 believed in heaven and a proportion of 0.73 believed in hell.
A 2013 article in the journal Adolescent Health stated that adding energy drinks to alcohol was associated with an elevated blood alcohol content compared to consuming alcohol without energy drinks
Refer to part c in the previous exercise.a. Show that a 99% confidence interval is (10.0, 16.2).b. Explain why this interval is wider than the 95% confidence interval.Previous exercisec. Calculate
In 2014, the GSS asked, €œWhat is the ideal number of children for a family to have?€ For those giving a numerical response (and treating the response €œ7 or
A study on nicotine dependence for teenage smokers obtained a random sample of seventh graders. The response variable was constructed from a questionnaire called the Hooked on Nicotine Checklist
Refer to Exercise 10.23 about studying nicotine dependence using a random sample of teenagers. Of those seventh graders in the study who had tried tobacco, the mean HONC score was 2.8 (s = 3.6) for
In an experiment investigating body language (M. Koppensteiner et al., Personality and Individual Differences, vol. 74, 2015, pp. 182€“185), researchers turned short video clips of randomly
One of the authors of this book has his lung function checked every other year. At each checkup, his lung volume (called the forced vital capacity, or FVC) is measured before and after using an
Refer to Example 10, €œArthroscopic Surgery.€ Here we show MINITAB output comparing mean knee pain scores for the placebo (Group 1) to lavage arthroscopic surgery (Group 2)
Refer to Exercise 10.38, which compared two therapies for depression patients. Suppose that in a different experiment, only four patients took part; two were randomly assigned to the group that
Refer to the previous exercise comparing improvement scores under two therapies for depression patients.a. State the null hypothesis of equal population distributions in the context of this
Refer to the previous exercise and the sampling distribution mentioned there. What is the permutation P-value for the two-sided test with alternative hypothesis that the mean improvement scores are
Exercise 10.31 considered the following data on the number of hours students spent on social network sites per week:Enter the observations (separated by spaces) into the Permutation Test web app. Let
For a rating experiment, researchers translated short video clips of randomly selected speeches by 30 male and 30 female politicians into animated, gender-neutral stick-figures. These animated
Refer to Example 12, which compared two groups of seven dogs each in terms of their time interacting with their owners. The following graph shows a smoothed version of the sampling distribution of
Refer to Exercise 10.34 about measuring the lung function (called the forced vital capacity, or FVC, measured in liters) before and after using an inhaler. The data are shown again in the following
A study was conducted to see if an advertisement campaign would increase market share for Sanka instant decaffeinated coffee (R. Grover and V. Srinivasan, J. Marketing Research, vol. 24, 1987, pp.
Last month a random sample of 1000 subjects was interviewed and asked whether they thought the president was doing a good job. This month the same subjects were asked this again.The results are: 450
Refer to the previous exercise. Results in this poll also depended strongly on the country in which the question was asked. For instance, the percentages believing in (heaven, hell) were (52%, 26%)
A Pew Research Center survey of 2002 U.S. adults in August 2014 and a survey of 3748 scientists connected to the American Association for the Advancement of Science (AAAS) in September 2014 both
The Centers for Disease Control (www.cdc.gov) periodically administers large randomized surveys to track health of Americans. In a survey of 4431 adults in 2003/2004, 66% were overweight (body mass
The table shows results from the 2014 General Social Survey on gender and whether one believes in an afterlife.a. Denote the population proportion who believe in an afterlife by p1 for females and by
The 2014 GSS asked about the number of hours you watch TV per day. An analysis that evaluates this by race shows the results (note the codes: 1 = Black and 2 = White):a. Do you believe that TV
Geneticists hypothesized that one reason for a prolonged lifespan observed in yeast cells treated with the common drug ibuprofen stems from inhibiting the uptake of certain amino acids. In an
Explain why the correlation between x = number of years of education and y = annual income is likely to be smaller if we use a random sample of adults who have a Ph.D. than if we use a random sample
What assumptions are needed to use the linear regression model to a. Obtain a meaningful fit that represents the true relationship wellb. To make inferences about the relationship. For part b,
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 why the predicted U.S.
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 using x to predict y compared to
The correlation is appropriate for describing association between two quantitative variablesa. Even when different people measure the variables using different units (e.g., kilograms and pounds).b.
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 describe the strength of association.c.
The regression of y on x has a prediction equation of ŷ = -2.0 + 5.0x and a correlation of 0.3. Then, the regression of x on ya. Also has a correlation of 0.3.b. Could have a negative slope.c. Has
University of Rochester economist Steven Landsburg surveyed economic studies in England and the United States that showed a positive correlation between height and income. The article stated that in
The variables y = annual income (thousands of dollars), x1 = number of years of education, and x2 = number of years experience in job are measured for all the employees having city-funded jobs in
The following data (also available from the book€™s website) is from a random sample of campus newspaper ads on used cars for sale. Consider the age and horsepower (HP) of a car to predict
Let€™s use multiple regression to predict total body weight (TBW, in pounds) using data from a study of female college athletes. Possible predictors are HGT = height (in inches), %BF =
For the 19 used cars listed in the Used Cars data file on the book€™s website (see also Exercise 13.11), modeling the mean of y = used car price in terms of x1= age results in r2 = 0.66.
In the previous exercise, r2 = 0.66 when age is the predictor and R2 = 0.69 when both age and HP are predictors. Why do you think that the predictions of price don’t improve much when HP is added
Examples 4€“7 used multiple regression to predict total body weight of college athletes in terms of height, percent body fat, and age. The following figure shows a histogram of the
When we use multiple regression, what’s the purpose of doing a residual analysis? Why can’t we just construct a single plot of the data for all the variables at once to tell whether the model is
Refer to the used car data file from Exercise 13.11. The prediction equation relating y = selling price of used car (in $) as a function of x1 = age of car and x2 = type of car (1 = US, 0 = Foreign)
Refer to Exercise 13.41, with ŷ = predicted selling price of used car and x1 = age of car. When equations are fitted separately for U.S. and foreign cars, we get ŷ = 23,417 - 1,715x1 for U.S.
Consider predicting the per capita GDP (gross domestic product, in thousands of dollars), of a country, using x1= carbon dioxide emissions per capita (in metric tons) and x2= percent of country
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 stated: “A linear
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 since 1994 (e.g., x = 0 for
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 second round, what
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 the mean of y at a
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 necessary assumptions, find a 95%
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 the interpretation of r2
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 the 99th percentile on performance) and
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 of the
Although the slope does not measure association, it is useful for comparing effects for two variables that have the same units. For the Internet Use data file of 32 nations on the book’s website,
If a slope is 1.50 when x = income in thousands of dollars, then what is the slope when x = income in dollars?
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 explanatory variable.
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 square feet to 4,050 square feet.a.
Whether a young married woman becomes pregnant in the next year is a categorical variable with categories (yes, no). Another categorical variable to consider is whether she and her partner use
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 (measured in grams) of
A recent survey of Austrian high school students asked whether it makes sense for 16-year-olds to be allowed to vote in the next parliamentary election. The following table shows results.a. Verify,
For testing independence in a contingency table of size r Ã— c, the degrees of freedom (df) for the chi-squared distribution equal df = (r - 1) Ã— (c - 1). They have the
Even when the sample conditional distributions in a contingency table are only slightly different, when the sample size is very large it is possible to have a large X2 statistic and a very small
Refer to a contingency table that cross-classifies subjects in tworows and two columns (labeled Success and Failure) and for which the odds ratio equals 4. True or False: Subjects in row 1 are 4
Interchanging the rows in a 2 × 2 contingency table has no effect on the value of the relative risk.
Interchanging two rows or interchanging two columns in a contingency table has no effect on the value of the X2 statistic.
The null hypothesis for the test of independence between two categorical variables is H0: X2 = 0 for the sample chi-squared statistic X2.
According to recent United Nations figures, the annual intentional homicide rate is 4.7 per 100,000 residents in the United States and 1.0 per 100,000 residents in Britain.a. Compare the proportion
Give an example of a contingency table for which the chi-squared test of independence should not be used.
When looking at a collection of numbers, such as population sizes, the figures on tax returns or the charges on a credit card, one may think that the leading digit of the number is equally likely to
Give an example of three variables for which you expect β ≠ 0 in the model μy = α + βx1 but β1 = 0 in the model μy = α + β1 x1 + β2 x2.
Multiple choice: Interpret parameter If ŷ = 2 + 3x1 + 5x2 - 8x3, then controlling for x2 and x3, the change in the estimated mean of y when x1 is increased from 10 to 20a. Equals 30.b. Equals
Refer to Exercise 13.67. When unemployment rate of a country is added as an additional predictor to the model already containing CO2 and percentage of population not using the Internet, we get the
In the model μy = α + β1 x1 + β2 x2, suppose that x2 is an indicator variable for gender, equaling 1 for females and 0 for males.a. We set x2 = 0 if we want a predicted mean without knowing
Multiple regression is used to model y = annual income using x1 = number of years of education and x2 = number of years employed in current job.a. It is possible that the coefficient of x2 is
For two studies, each comparing three groups, the box plots below show results. (Each box plot is based on a random sample of size 40.)a. Judging from the box plots, which study will more likely lead
The restaurant guide Zagat compiles customer ratings on the quality of food on a 30-point scale. The data set French Cuisine on the book’s website contains a random sample of ratings of French
The Anorexia data file on the book’s website shows weight change for 72 anorexic teenage girls who were randomly assigned to one of three psychological treatments (cognitive or family therapy and a
For the House Selling Prices OR data file on the book€™s website, the output shows the result of conducting an ANOVA comparing mean house selling prices (in $1000) by Age Category (New = 0
Do freshmen spent significantly more time on Facebook than other class ranks? A recent study (R. Junco, Journal of Applied Developmental Psychology, 2015, vol. 36, p. 18€“29) investigated
Refer to Exercise 14.13, which investigated the amount of time freshman, sophomores, juniors, and seniors spent on Facebook while doing schoolwork. The data from the study are available on the
The GSS measures political ideology on a seven-point scale, starting with 1 = extremely liberal, to 4 = moderate, to 7 = extremely conservative. The following table shows results from an ANOVA
For the House Selling Prices OR data file on the book€™s website, the output shows the result of conducting a two-way ANOVA of house selling prices (in thousands) by the number of bedrooms
In 2012, the population mean hourly wage for males was $17 for high school graduates, $33 for college graduates and $43 for males with more advanced degrees. For females, the means were $14 for high
The 2014 General Social Survey asked 1475 subjects how many hours per day they watched TV, on average. Are there differences in population means according to the marital status of the subject
Refer to the previous exercise.a. Using software, find the margin of error that pertains to each comparison, using the Tukey method for 95%multiple comparison confidence intervals.b. Using part a,
Refer to the House Selling Price OR data file on the book’s website.a. The variable “Garage” included in the data set is an indicator variable for whether a house has a garage (with 1
In a class experiment at Williams College, students were randomly assigned either to drink or abstain from drinking an energy drink before attempting a straightforward but tedious mathematical task.
A study on the effects of prenatal exposure to smoke (by J. Nigg and N. Breslau, Journal of the American Academy of Child & Adolescent Psychiatry, vol. 46, 2009, pp. 362–369) indicated that
The first table shown summarizes responses on political ideology (where 1 = extremely liberal and 7 = extremely conservative) from the 2014 GSS by gender and race.a. From these sample means, is there
When we use the 2014 GSS and regress y = number of hours per day watching TV on g = gender (1 = male, 0 = female) and marital status (m1= 1 for singles, 0 otherwise, m2= 1 for married subjects, 0
Using the GSS website sda.berkeley.edu/GSS, analyze whether the number of good friends (the variable NUMFREND) depends on the subject’s highest degree (the variable DEGREE). To do so, click the
In multiple comparisons following a one-way ANOVA with equal sample sizes, the margin of error with a 95% confidence interval for comparing each pair of means equals 10. Give three sample means
Analysis of variance and multiple regression have many similarities. Which of the following is not true? a. The response variable is quantitative for each.b. They both have F tests for testing
One-way ANOVA provides relatively more evidence that H0: μ1 = ...= μg is false:a. The smaller the between-groups variation and the larger the within-groups variation.b. The smaller the
For four means, it is planned to construct Tukey 95% multiple comparison confidence intervals for the differences between the six pairs.a. For each confidence interval, there is a 0.95 chance that
There is interaction in a two-way ANOVA model whena. The two factors are associated.b. Both factors have significant effects in the model without interaction terms.c. The difference in true means
For subjects aged under 50, there is little difference in mean annual medical expenses for smokers and nonsmokers. For subjects aged over 50, there is a large difference. Is it true or false that
An experiment used four groups of five individuals each. The overall sample mean was 60.a. What did the sample means look like if the one-way ANOVA for comparing the means had test statistic F = 0?b.
Present a situation for which it’s preferable to use a nonparametric method instead of a parametric method and explain why.
For a one-sided significance test comparing two means with small samples from highly skewed population distributions, it’s safer to use a t test than a Wilcoxon test. This is because the Wilcoxon
Describe the advantages of an experiment using a crossover design instead of independent samples to compare the tanning methods.
The t test for comparing two means is to the one-way ANOVA F test as the Wilcoxon test is to the __________ test.
The t test for comparing two means is to the Wilcoxon test (for independent samples) as the matched pairs t test is to the __________ (for dependent samples in matched pairs).

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