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mathematics
statistics the art and science

Questions and Answers of Statistics The Art and Science

Use data collected from a sample of applicants at a college admissions office to measure how large the difference is in the average size of the financial aid package between early decision applicants
Use data from a study done at a college fitness center in which muscle mass of participants was measured before and after a 6-week program working with resistance bands to estimate the mean increase
Use a sample of students at a large university to determine whether the proportion of students at the university who are left-handed is different from the national US proportion of 12%.Identify the
Use results from a survey to estimate the difference in the proportion of males and females who say they are trying to lose weight.Identify the method of analysis needed to answer the question.
A recent headline states that ‘‘73% say Woman President Likely in Next 10 Years.” The report gives the results of a survey of 1000 randomly selected likely voters in the US. Find and interpret
Can rats feel empathy toward fellow rats? In a recent study, some rats were first habituated to two chambers: a witness chamber adjacent to a shock chamber. The experimental rats (n = 15) were then
In Exercise B.6 on page 306 we look at some data on the results of overtime games in the National Football League (NFL) from 1974 through the 2009 season. The question of interest is how much
Find and interpret a 90% confidence interval for the proportion of times a lie detector accurately detects a lying person.Refer to the data in Table C.5. These data, introduced in Exercise A.23 on
Test to see if there is evidence that the lie detector says a person is lying more than 50% of the time, regardless of what the person reads. Refer to the data in Table C.5. These data,
Test to see if there is a difference in the proportion the lie detector says is lying depending on whether the person is lying or telling the truth.Refer to the data in Table C.5. These data,
Find and interpret a 95% confidence interval for the difference in the proportion the lie detector says is lying between those lying and those telling the truth.Refer to the data in Table C.5. These
Asurvey conducted of 1502 randomly selected US adults found that 931 of them believed the government does not provide enough support for soldiers returning from Iraq or Afghanistan. Use this
Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Exercises 2.51 and 2.103 on pages 71 and 87, respectively, describe an
Exercise 2.25 on page 57 introduces a study investigating whether smoking might negatively effect a person€™s ability to become pregnant. The study collected data on 678 women who had gone
In the StudentSurvey data, there are 36 seniors: 26 males and 10 females. Table C.9 gives the number of hours per week that each said he or she spent exercising. Find a 95% confidence interval for
Exercise A.32 on page 149 introduces a study investigating the effectiveness of behavioral changes and prescription medication in helping older people find improvement in fighting insomnia. The
The typical resting pulse rate in adults is 60 to 80 beats per minute. For the 200 Intensive Care Unit patients in the dataset ICUAdmissions, the average pulse rate in the sample is x̅ = 98.9 bpm
Honeybee colonies have specific ‘‘scout” honeybees, that are entrusted with finding new sites for hives. The mean age of honeybees in a hive is about 12 days. In a sample of 50 scout honeybees,
Tribulus is a food supplement that some athletes use to enhance performance. A study on the effects of this supplement involved randomly assigning 20 athletes to take the supplement for a 20 day
CAOS Comparisons Anarticle by the developers of the CAOS exam described in Exercise C.68 gives benchmark data based on a very large number of students taking the CAOS pretest and posttest. The mean
We have seen in earlier exercises that the conditions are met for using a regression line to predict the Tip from the size of the Bill. Some regression output is shown for fitting this linear
ANOVA for difference in means for 100 people separated into six groups with F-statistic = 2.51A test statistic for one of the tests in this unit is given, along with information about sample size(s)
A two-tailed test for the coefficient of the first predictor in a three-predictor regression model with t-statistic = 1.83 and n = 26A test statistic for one of the tests in this unit is given, along
Testing to see if there is evidence that the mean time spent studying per week is different between first-year students and upperclass students.Describe how you might physically create one
Testing to see if average sales are higher in stores where customers are approached by salespeople than in stores where they aren’t.Describe how you might physically create one randomization sample
Testing to see if there is evidence that the percentage of a population who watch the Home Shopping Network is less than 20%.Describe how you might physically create one randomization sample and
Testing to see if there is evidence that a correlation between height and salary is significant (that is, different than zero.)Describe how you might physically create one randomization sample and
Testing to see if there is evidence that the proportion of people who smoke is greater for males than for females.Describe how you might physically create one randomization sample and compute one
Use StatKey or other technology to create the randomization distribution for the situation in Exercise B.48. Use the distribution to calculate a p-value. Using α = 0.05, state the conclusion in
The dataset FloridaLakes is introduced in Data 2.4 on page 68, and we return to the dataset in Exercise B.45 on page 315. To see if there is evidence of a negative correlation between pH in lakes and
Exercise B.38 on page 314 describes a randomized trial in South Africa to test whether the proportion of babies born with infections is smaller if women in labor are treated with a wipe containing
In Data 4.5 on page 228 we describe a situation in which a restaurant chain will test for arsenic levels in a sample of chickens from a supplier. If there is evidence that the average level of
Exercise 3.84 on page 204 describes the variable Distance for the Atlanta commuter sample stored in CommuteAtlanta, giving the distance of each commute (in miles). Use StatKey or other technology to
It is estimated that in the general population about 9 out of every 1000, or 0.009, children are diagnosed with autism. A recent study included 92 six-month-old babies who had a sibling with autism.
In Exercise B.40, we learn that when 48 stressed individuals read a truthful passage while being hooked up to a lie detector, the lie detection software inaccurately reported deception by 27 of them.
Is lie detection software accurate? Exercise A.23 on page 147 describes a study in which 48 individuals read a truthful passage while under stress and while connected to a lie detector. The lie
In Exercise 3.52 on page 189, we discuss a Gallup poll stating that the proportion of American adults getting health insurance from an employer is estimated to be 0.45. We are also told that, with
The Centers for Disease Control and Prevention (CDC) conducted a randomized trial in South Africa designed to test the effectiveness of an inexpensive wipe to be used during childbirth to prevent
Does heavy cell phone use increase the incidence of brain tumors? Astudy of cell phone use among 10,000 participants found that ‘‘the 10% who used their phones most often and for the longest time
Data 2.7 on page 93 introduces the dataset HollywoodMovies2011, which contains information on all the 136 movies that came out of Hollywood in 2011.(a) Find the mean and standard deviation for the
Internet One of the variables in the AllCountries dataset gives the percent of the population of each country with access to the Internet. This information is available for all 199 countries
Exercise B.33 describes a study on the use of ketamine in treating depression in mice. Ten depressed mice given the drug had a mean score of 135 seconds on a forced-swim test used to measure
Traditional antidepressants often take weeks or months to improve symptoms. A new study may provide a faster acting option. The anesthetic ketamine is very dangerous and can be deadly at high doses.
The Super Bowl is the final championship game in the National Football League in the US and is one of the most watched television events of the year. In January 2016, just before Super Bowl 50, a
In Example 3.25 on page 207, we compare the mean hours of exercise per week between male and female college students. The sample results are included in the dataset Exercise Hours, where we see that
What is the expected center of a bootstrap distribution generated to find a confidence interval? What is the expected center of a randomization distribution generated to test a hypothesis?
Exercises B.24 and B.25 describe a study to determine whether a sales tax on soda will reduce consumption of soda in the US below the current per-capita level of about 50 gallons of soda per year.
From its founding through 2012, the Rock and Roll Hall of Fame has inducted 273 groups or individuals, and 181 of the inductees have been performers while the rest have been related to the world of
Given a specific sample to estimate a specific parameter from a population, what are the expected similarities and differences in the corresponding sampling distribution (using the given sample size)
Data 2.7 on page 93 introduced the dataset Hollywood- Movies2011, which contains information on all the 136 movies that came out of Hollywood in 2011. Thirty-two of the Hollywood movies that year
We extend the situation described in Exercise B.24 to each of the pairs of boxplots in Figure B.9. In each case, indicate whether the results of Sample A or Sample B show stronger evidence that
The average American drinks approximately 50 gallons of soda (pop) a year, delivering approximately 50,000 calories and no nutrition. Some legislators are recommending instituting a sales tax on soda
Exercise B.22 discusses a study to see if smoking might be negatively related to a woman€™s ability to become pregnant. The study looks at the proportion of successful pregnancies in two
Exercise 2.25 on page 57 introduces a study of 678 women who had gone off birth control with the intention of becoming pregnant. Table B.6 includes information on whether or not a woman was a smoker
According to a recent survey, most Americans prefer to watch a movie in the comfort of their own home rather than going out to a theater. In the telephone survey of 1000 randomly selected American
We select a random sample of n = 10 textbooks at a university bookstore and are testing to see if there is evidence that the average price of textbooks at that store is greater than $100. Give an
A pizza delivery person was interested in knowing how she spends her time and what her actual hourly earnings are, so she recorded all of her deliveries and tips and how she spent every minute of her
In Example 3.17 on page 186, we learn that, in a random sample of over 450,000 US adults, the proportion of people who say they exercised at some point in the last 30 days is p̂ = 0.726 with a
Many professors do not like having cell phones ring during class. A recent study appears to justify this reaction, by showing that a ringing cell phone can adversely affect student learning. In the
The dataset HollywoodMovies2011 contains information on all 136 movies to come out of Hollywood in 2011. We see in Exercise B.13 that 27 of the movies were comedies. If we take 1000 samples of size n
Data 2.7 on page 93 introduces the dataset HollywoodMovies2011, which contains information on all 136 movies to come out of Hollywood in 2011. Twenty-seven of those movies were comedies.(a) What
Scientists hoping to curb deforestation estimate that the carbon stored in tropical forests in Latin America, sub-Saharan Africa, and southeast Asia has a total biomass of 247 gigatons spread over
A recent national telephone survey reports that 57% of those surveyed think violent movies lead to more violence in society. The survey included a random sample of 1000 American adults and reports:
Exercise B.8 describes data on ages of husbands and wives at the time of marriage.(a) Do you expect the correlation between the ages at marriage of husbands and wives to be positive, negative, or
A sample of marriage licenses from 2010 to 2011 in St. Lawrence County in Northern New York State gives the ages of husbands and wives at the time of marriage for 105 newly married couples. The data
How much of an effect does your roommate have on your grades? In particular, does it matter whether your roommate brings a videogame to college? A study examining this question looked at n = 210
Overtime The National Football League (NFL) has used a sudden death overtime period since 1974 to help decide a winner in games that are tied at the end of regulation time. Before the overtime
Calcium Arecent study examined the effect of diet cola consumption on calcium levels in women. A sample of 16 healthy women aged 18 to 40 were randomly assigned to drink 24 ounces of either diet cola
Can dogs provide an easy noninvasive way to detect cancer? Several methods have been used to test this. In a recent study,50 five dogs were trained over a three week period to smell cancer in breath
A study conducted on a college campus tested to see whether students with colds who are given large doses of vitamin C recover faster than students who are not given the vitamin C. The p-value for
For each question, indicate whether it is best assessed by using a confidence interval, a hypothesis test, or whether statistical inference is not relevant to answer it. If inference is not relevant,
For each question, indicate whether it is best assessed by using a confidence interval, a hypothesis test, or whether statistical inference is not relevant to answer it. If inference is not relevant,
The dataset HomesForSale has data on houses available for sale in three Mid- Atlantic states (NY, NJ, and PA) and California (CA). We are interested in the proportion of Mid- Atlantic houses that are
The dataset HomesForSale has data on houses available for sale in three Mid-Atlantic states (NY, NJ, and PA) as well as California (CA). In Exercise C.62 we see that in the sample of 90 Mid- Atlantic
Table C.13 gives systolic blood pressure readings (first introduced in Exercise A.36 on page 150) for Intensive Care Unit patients in their teens and those in their eighties.Table C.13(a) Find and
Patients Exercise 2.135 on page 100 discusses a study showing the recurrence time to infection at the point of insertion of the catheter for kidney patients using portable dialysis equipment. There
The Comprehensive Assessment of Outcomes in Statistics (CAOS) exam is an online multiple-choice test on concepts covered in a typical introductory statistics course. Students can take a pretest
Some computer output is shown on the next page from an analysis to compare mean commute time between males and females using data from St. Louis commuters in CommuteStLouis. Write a paragraph
Exercise C.70 gives computer output comparing mean commute time between males and females in the city of St. Louis. Use the data in CommuteAtlanta to see if a similar relationship (or lack of
Dr. Jeremy Groves, a British anaesthetist, often uses a bicycle for his 27-mile round-trip commute to work. He bought an expensive, lightweight, carbon bike but also had an older, heavier, steel
Exercise B.8 on page 307 introduces the MarriageAges dataset that contains the ages for husbands and wives from a sample of 105 marriage licenses in St. Lawrence County, New York. In that exercise we
Refer to Exercise C.73 for a description of the data in Marriage Ages for a sample of 105 newly married couples.(a) Use technology to find the mean age for the wives in this sample and construct a
Exercise 2.144 on page 102 describes a study conducted by engineers in Dresden, Germany looking at ways to improve traffic flow by enabling traffic lights to communicate with each other in real time.
The data come from three different servers, coded as A, B, and C to preserve anonymity. The number of bills for each server is shown in Table D.5. Do the servers serve equal numbers of tables?Table
The number of bills for each day of the week is shown in Table D.6. Does this provide evidence that some days of the week are more popular (have more bills) than others?Table D.6In Data 2.12 on page
The data come from three different servers, coded as A, B, and C, and we also have information on whether or not a credit (or debit) card was used to pay the bill rather than cash. The frequency
The data come from all five week days and we also have information on whether or not a credit (or debit) card was used to pay the bill rather than cash. The frequency counts are shown in the two-way
Most restaurant patrons leave a tip between 15% and 20% of the bill, and some restaurant customers determine the percent tip to leave based on the quality of service. Summary statistics for mean tip
Are some servers given the big spenders (or large groups) while others tend to those having only a cup of coffee or a glass of wine? Is there a difference in the mean size of the bill between the
Do larger parties tend to leave a larger tip? Figure D.3 shows a scatterplot between the size of the tip and the number of guests.Figure D.3(a) Does there appear to be an association in the data
How much larger do tips get with larger parties? Figure D.3 shows a scatterplot between the size of the tip and the number of guests. Output regressing Tip on Guests is shown below:Figure D.3Residual
In Exercise D.9, we use the size of the bill to predict the tip. In this exercise, we use both the size of the bill and the number of guests to predict the size of the tip. Some regression output is
An upper-tail test for correlation with t-statistic = 1.36 and df = 15A test statistic for one of the tests in this unit is given, along with information about sample size(s) or degrees of freedom.
An analysis of variance test with F-statistic = 7.42 and df-numerator= 3 and df-denominator= 56A test statistic for one of the tests in this unit is given, along with information about sample size(s)
A chi-square goodness-of-fit test with χ2-statistic = 4.18 and 5 groupsA test statistic for one of the tests in this unit is given, along with information about sample size(s) or degrees of freedom.
A two-tailed test for slope in a one-predictor regression model with t-statistic = 2.89 and n = 30A test statistic for one of the tests in this unit is given, along with information about sample
A chi-square test for a 2 × 4 table with χ2-statistic = 6.83A test statistic for one of the tests in this unit is given, along with information about sample size(s) or degrees of freedom. Give the
A lower-tail test for correlation with t-statistic = −4.51 and n = 81A test statistic for one of the tests in this unit is given, along with information about sample size(s) or degrees of freedom.
Three different drugs are being tested on patients who have leukemia and the response variable is white blood cell count.In this unit, we have covered six specific tests, listed below. For each
Three different drugs are being tested on patients who are HIV-positive and the response variable is whether or not the person develops AIDS.In this unit, we have covered six specific tests, listed

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