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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

Year and the world record time in a marathon.A relationship between two variables is described. In each case, we can think of one variable as helping to explain the other. Identify the explanatory
Blood alcohol content (BAC) and number of alcoholic drinks consumed.A relationship between two variables is described. In each case, we can think of one variable as helping to explain the other.
Amount of fertilizer used and the yield of a crop.A relationship between two variables is described. In each case, we can think of one variable as helping to explain the other. Identify the
Lung capacity and number of years smoking cigarettes.A relationship between two variables is described. In each case, we can think of one variable as helping to explain the other. Identify the
Record whether or not the literacy rate is over 75% for each country in the world.(a) What are the cases?(b) What is the variable and is it quantitative or categorical?
Estimate the bending strength of beams by bending 10 beams until they break and recording the force at which the beams broke.(a) What are the cases?(b) What is the variable and is it quantitative or
Measure the shelf life of bunches of bananas (the number of days until the bananas go bad) for a large sample.(a) What are the cases?(b) What is the variable and is it quantitative or categorical?
Collect data from a sample of teenagers with a question that asks ‘‘Do you eat at least five servings a day of fruits and vegetables?”(a) What are the cases?(b) What is the variable and is it
Record the percentage change in the price of a stock for 100 stocks publicly traded on Wall Street.(a) What are the cases?(b) What is the variable and is it quantitative or categorical?
People in a city are asked if they support a new recycling law.(a) What are the cases?(b) What is the variable and is it quantitative or categorical?
Ebola virus disease outbreaks have a case fatality rate of 90% (meaning 90% of people who get it die). In a hospital that is treating 20 patients with ebola, 14 died. Is this result surprising? To
A political scientist at the University of Chicago studied the effect of the race of the interviewer.7 Following a phone interview, respondents were asked whether they thought the interviewer was
Hazing within college fraternities is a continuing concern. Before a national meeting of college presidents, a polling organization is retained to conduct a survey among fraternities on college
Based on the previous exercise and what you have learned in this and the previous chapter (for example, Exercise 5.12), if you are a serious investor, explain why you should not get too excited if
For a normally distributed random variable, the IQR is larger than the length of the interval μ ± σ
The table (data are available on the book’s website) provides prices per night for all 51 available hotel rooms (as of December 2014) in Panama City Beach, Florida, for a week in March 2015 (spring
Using the General Social Survey website sda.berkeley.edu/GSS with YEAR(2008) as the filter, find the point estimate of the population proportion of Americans who would have answered “yes,
Refer to the previous exercise. The margin of error for a 95% confidence interval for the population mean is 0.12. Construct that confidence interval and interpret it.Previous exerciseThe GSS has
Go to sda.berkeley.edu/ GSS and find a variable that is associated with happiness, other than variables used in this chapter. Use methodsfrom this chapter to describe and make inferences about the
Exercise 11.1 showed a 2 Ã— 3 table relating gender and political party identification, shown again here. The chi-squared statistic for these data equals 10.04 with a P-value of 0.0066.
For the table on marital happiness in Exercise 11.32, the chi-squared statistic equals 214 (df = 4, P-value < 0.0001). Explain the difference between the purposes of the chi-squared test in part a
Refer to the previous exercise. Height has a similar estimated slope for each of the three models. Why do you think that controlling for % body fat and then age does not change the effect of height
Consider the relationship between ŷ = annual income (in thousands of dollars) and x1 = number of years of education by x2 = gender. Many studies in the United States have found that the slope for a
Refer to the previous exercise which asked for the distribution of the number of games played in a best of 5 series when team A wins with probability 50%.a. Find the expected number of games played
A newspaper wants to gauge public opinion about legalization of marijuana. The sample size formula indicates that it need a random sample of 875 people to get the desired margin of error. But surveys
You would like to find the proportion of bills passed by Congress that were vetoed by the president in the last congressional session. After checking congressional records, you see that for the
In 2014, the General Social Survey asked about the number of hours a week spent on the World Wide Web (variable denoted WWWHR). Some results are as follows:a. Identify the response variable and
In the United States, is there a gender gap in political beliefs? That is, do women and men tend to differ in their political thinking and voting behavior? The table taken from the 2012 GSS relates
Data from 2013 posted on the Williams College website shows that of all 3,195 males applying, 18.2% were admitted, and of all 3,658 females applying, 16.9% were admitted. Let X denote gender of
The contingency table shown relates happiness and gender for the 2012 GSS.a. Identify the response variable and the explanatory variable.b. Construct a table or graph showing the conditional
In the GSS, subjects who were married were asked about the happiness of their marriage, the variable coded as HAPMAR.a. Go to the GSS website sda.berkeley.edu/GSS/, click GSS with no weight as the
In the 2012 GSS, 605 of 790 males and 822 of 977 females indicated a belief in life after death. (Source: Data from CSM, UC Berkeley.)a. Construct a 2 × 2 contingency table relating gender of
For the 2 Ã— 3 table on gender and happiness in Exercise 11.4 (shown below), software tells us that X2= 1.04 and the P@value = 0.59.a. State the null and alternative hypothesis, in
How large an X2 test statistic value provides a P-value of 0.05 for testing independence for the following table dimensions?a. 2 × 2b. 2 × 3c. 2 × 5d. 5 × 5e. 3 × 9
In Exercise 11.5 when you used the GSS to download a 3 Ã— 3 table for family income and marital happiness in 2012, you should have obtained results similar to the following table.a. State
In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither
For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates (such as snails, insects, or crayfish), birds
The study mentioned in Example 5 also looked at the severity of fever (rated as mild, moderate or severe) for all subjects who developed one after receiving a flu shot. The following table shows
Based on a random sample of 84 students taken at Williams College, the table shows how many had their birthday in the first, second, third, or fourth quarter of the year. Is there evidence that the
The two tables show 2012 GSS data on whether someone is identified as Democrat, by race and by gender.a. Find the difference of proportions between blacks and whites and between females and males.
Table 11.10, summarized again here, showed the associations between death penalty opinion and gender or race.a. True or false: The table with the larger X2 statistic necessarily has the stronger
The table refers to a survey of senior high school students in Dayton, Ohio. It cross-tabulates whether a student had ever smoked cigarettes and whether a student had ever drunk alcohol and shows
For murders in the United States in 2012, the table cross-tabulates the sex of the victim by the sex of the offender. Find and interpret a measure of association, treating sex of victim as the
A recent study (Pinto et al., Olfactory Dysfunction Predicts 5-Year Mortality in Older Adults. PLoS ONE 9(10):e107541, 2014) mentions that anosmic (those with almost no sense of smell) older adults
In September 2004, the pharmaceutical company Merck withdrew its blockbuster drug rofecoxib (a painkiller, better known under its brand name, Vioxx) from the worldwide market amid concerns about its
When comparing the cell-derived flu vaccine mentioned in Example 9 to a more traditionally manufactured egg-derived vaccine, the following data were obtained.a. Find the relative risk of developing
The table shows 2012 GSS data on marital and general happiness for married respondents.a. The chi-squared test of independence has X2 = 214. What conclusion would you make using a significance level
The table shows the 2012 GSS data on gender and political party identification from Exercise 11.1. (The row totals are slightly different from the second table in Exercise 11.24 because selecting
The table displays the observed and expected cell counts and the standardized residuals for testing independence of happiness and family income, for GSS data.a. How would you interpret the
Exercise 11.32 showed the association between general happiness and marital happiness. The table shown here gives the standardized residuals for those data in parentheses.a. Explain what a relatively
The screen shot from the GSS website shows standardized residuals (called Z-statistics) and cell counts for 2012 GSS data on happiness (the column) and marital status (the row). The color coding is
The table in Exercise 11.1 on gender and party identification is shown again. The largest standardized residuals in absolute value were +2.98 for females who identified as Democrats and -2.98 for
To help students gauge their understanding of basic concepts, short online quizzes with immediate feedback were administered in an introductory statistics (STAT) and an unrelated computer science
Refer to the previous exercise. After the semester, students were asked whether the quizzes were beneficial, with possible answers (i) Yes, I realized that I knew more than I thought,(ii)Yes, I
The following table, on the presence of pesticide residues in samples of organic and conventional food, was analyzed in Examples 2 and 3 in Chapter 3.a. Compute the relative risk and interpret.b.
When crossing round (R) and yellow (Y) peas with wrinkled (W) and green (G) peas, one can get any combination of color and appearance, denoted here as RY, RG, WY and WG, but traits round and yellow
In 2007, the FDA announced that the popular drug Zelnorm used to treat irritable bowel syndrome was withdrawn from the market, citing concerns about serious side effects. The analysis of several
A contingency table from the 2012 GSS relating happiness to number of sex partners in the previous year (0, 1, at least 2) had standardized residuals (called Z-statistic here) as shown in the screen
Does the clarity of a diamond depend on its cut? Exercise 3.4 showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly
Refer to Example 11, which compared two doses of a medication in terms of the number of symptom-free days, using a permutation approach. Table 10.13 and Figure 10.9 showed the sampling distribution
True or false. The power of a test = 1 - P(Type II error).
A study about the change in weight on a new diet reports P@value = 0.043 for testing H0: μ = 0 against Ha: μ ≠ 0. If the authors had instead reported a 95% confidence interval for m, then the
It is always the case that P(Type II error) = 1 - P(Type I error). True or false.
In the previous exercise, suppose you had predicted that if the mean changed, it would have increased above the control value. State the alternative hypothesis for this prediction and report and
For each of the following scenarios, define the parameter of interest and appropriate null and alternative hypotheses.a. To motivate more fathers to take a parental leave, the government of Austria
A null hypothesis states that the population proportion p of headache sufferers who have better pain relief with aspirin than with another pain reliever equals 0.50. For a crossover study with 10
Refer to the previous exercise. The following figure is a residual plot for the model relating maximum bench press to LP200 and BP60. It plots the standardized residuals against the values of BP60.
The 49 students in a class at the University of Florida made blinded evaluations of pairs of cola drinks. For the 49 comparisons of Coke and Pepsi, Coke was preferred 29 times. In the population that
According to an exit poll of the 2010 California gubernatorial election (see Chapter 7), 53.1% of the 3889 voters sampled reported voting for Brown. Is this enough evidence to predict who won? Test
Refer to the 95% confidence interval shown in the MINITAB output in the previous exercise. What are the plausible values for the probability of a female to be selected for training? Is this in
For a large supermarket chain in Florida, a women€™s group claimed that female employees were passed over for management training in favor of their male colleagues. The company denied this
The question about the opinion on the increased use of fracking from the November 2014 survey mentioned in Example 6 was also included in an earlier survey in September 2013. Using this earlier
Americans ages 18 to 29 are considered to be less religious than older Americans. According to recent studies by the Pew Forum on Religion & Public Life, fewer young adults are affiliated with a
A person who claims to be psychic says he predicts the outcome of a flip of a fair coin more often right than wrong. If we want to test this claim, we could use the data from an experiment in which
Indicate whether each of the following P-values gives strong evidence or not especially strong evidence against the null hypothesis.a. 0.38b. 0.001
To test H0: p = 0.50 that a population proportion equals 0.50, the test statistic is a z-score that measures the number of standard errors between the sample proportion and the H0 value of 0.50. If z
Explain what is wrong with each set of null and alternative hypotheses shown. Then, correct each to form a proper set of hypotheses.a. H0: p̂ = 0.50, Ha: p̂ > 0.50b. H0: μ = 100, Ha: μ =
The average financial aid package for students admitted at Williams College in 2010 was $44,000. A student organization plans to investigate whether this average has changed for students admitted in
For a new pesticide, should the Environmental Protection Agency (EPA) bear the burden of proof to show that it is harmful to the environment, or should the producer of the pesticide have to show that
For each of the following, is the statement a null hypothesis or an alternative hypothesis? Why?a. The mean IQ of all students at Lake Wobegon High School is higher than 100.b. The probability of
Consider the sample size formula n = [p̂ (1 – p̂)z2]/m2 for estimating a proportion. When p̂ is close to 0.50, for 95% confidence explain why this formula gives roughly n = 1/m2.
A special issue of Newsweek in March 1999 on women and their health reported results of a poll of 757 American women aged 18 or older. When asked, “How satisfied are you with your overall physical
True or false. Quadrupling the sample size n cuts the margin of error into half, other things being equal.
True or false. If you have a volunteer sample instead of a random sample, then a confidence interval for a parameter is still completely reliable as long as the sample size is larger than about 30.
True or false. The confidence interval for a mean with a random sample of size n = 2000 is invalid if the population distribution is bimodal.
Suppose a 95% confidence interval for the population proportion of students at your school who regularly drink alcohol is (0.61, 0.67). The inference is that you can be 95% confident that the sample
For the previous exercise, provide the proper interpretation.Previous exerciseA random sample of 50 records yields a 95% confidence interval of 21.5 to 23.0 years for the mean age at first marriage
The reason we use a z-score from a normal distribution in constructing a large-sample confidence interval for a proportion is thata. For large random samples the sampling distribution of the sample
Based on responses of 1467 subjects in a General Social Survey, a 95% confidence interval for the mean number of close friends equals (6.8, 8.0). Which two of the following interpretations are
Other things being equal, increasing n causes the margin of error of a confidence interval to (a) Increase, (b) Decrease, (c) Stay the same.
Increasing the confidence level causes the margin of error of a confidence interval to a. Increase, b. Decrease, c. Stay the same.
For the observations 618, 650, 608, 634, 675, 618, 625, 619, 630 on Buy It Now prices for the iPhone 5s on eBay considered in Exercise 8.35, a confidence interval for the population mean Buy It Now
Explain why confidence levels are usually large, such as 0.95 or 0.99, but not extremely large, such as 0.999999.
For a trip to Miami, Florida, over spring break 2014, the following data (obtained from travelocity.com) are a random sample of hotel prices per night (in $) for a double room:a. Construct a
In response to the statement on a recent General Social Survey, â€œA preschool child is likely to suffer if his or her mother works,â€ suppose the response categories (strongly agree, agree,
Refer to the previous exercise. The 626 males had a mean of 2.87 and a standard deviation of 2.61. The 95% confidence interval for the population mean is (2.67, 3.08). Interpret in context.Previous
For eBay auctions of the Samsung S5 16GB smartphone (unlocked and in new condition), a sample was taken in July 2014 where the Buy It Now prices were (in dollars):549, 600, 560, 519, 535, 570, 600,
The government website fuel economy. gov has data on thousands of cars regarding their fuel efficiency. A random sample from this website of SUVs manufactured between 2012 and 2015 gives the
When the GSS asked in 2012, €œAbout how many hours per week do you spend sending and answering e-mail?€ the nine males in the sample of age at least 80 responded:0, 0, 0, 1, 2,
Refer to the previous exercise.a. Of the 1001 adults surveyed in Turkey, 49% said yes to the question from the Pew Research Center, resulting in a 95% confidence interval of (0.46, 0.52).True or

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