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Business Statistics
When we want \(95 \%\) confidence and use the conservative estimate of \(p=0.5\), we can use the simple formula \(n=1 /(M E)^{2}\) to estimate the sample size needed for a given margin of error \(M
When we want \(95 \%\) confidence and use the conservative estimate of \(p=0.5\), we can use the simple formula \(n=1 /(M E)^{2}\) to estimate the sample size needed for a given margin of error \(M
A margin of error of 0.04 .When we want \(95 \%\) confidence and use the conservative estimate of \(p=0.5\), we can use the simple formula \(n=1 /(M E)^{2}\) to estimate the sample size needed for a
A margin of error of 0.05 .When we want \(95 \%\) confidence and use the conservative estimate of \(p=0.5\), we can use the simple formula \(n=1 /(M E)^{2}\) to estimate the sample size needed for a
Determine whether it is appropriate to use the normal distribution to estimate the p-value. If it is appropriate, use the normal distribution and the given sample results to complete the test of the
Do Babies Understand Probability? Can babies reason probabilistically? A study investigates this by showing ten- to twelve-month-old infants two jars of lollipop-shaped objects colored pink or black.
An article noted that it may be possible to accurately predict which way a penalty-shot kicker in soccer will direct his shot. The study finds that certain types of body language by a soccer player -
For a \(N(60,10)\) distribution. Find the specified areas for a normal distribution.(a) The area to the right of 65(b) The area to the left of 48
For a \(N(15,5)\) distribution. Find the specified areas for a normal distribution.(a) The area to the right of 28(b) The area to the left of 12
For a \(N(160,25)\) distribution(a) The area to the right of 140(b) The area to the left of 200 Find the specified areas for a normal distribution.
Effect of Organic Soybeans after 5 Days After 5 days, the proportion of fruit flies eating organic soybeans still alive is 0.90 , while the proportion still alive eating conventional soybeans is 0.84
Effect of Organic Bananas after 25 Days After 25 days, the proportion of fruit flies eating organic bananas still alive is 0.42 , while the proportion still alive eating conventional bananas is 0.40
Effect of Organic Potatoes after 11 Days After 11 days, the proportion of fruit flies eating organic potatoes still alive is 0.68 , while the proportion still alive eating conventional potatoes is
Effect of Organic Soybeans after 8 Days After 8 days, the proportion of fruit flies eating organic soybeans still alive is 0.79 , while the proportion still alive eating conventional soybeans is 0.32
Dogs Ignore an Unreliable Person A study investigated whether dogs change their behavior depending on whether a person displays reliable or unreliable behavior. Dogs were shown two containers, one
Incentives to Exercise: How Well Do They Work? A study was designed to see what type of incentive might be most effective in encouraging people to exercise. In the study, 281 overweight or obese
Incentives to Exercise: What Works Best? In the study described in Exercise 5.29, the goal for each of the overweight participants in the study was to walk 7000 steps a day. The study lasted 100 days
Incentives for Quitting Smoking: Group or Individual? In a smoking cessation program, over 2000 smokers who were trying to quit were randomly assigned to either a group program or an individual
Incentives for Quitting Smoking: Do They Work? Exercise 5.31 describes a study examining incentives to quit smoking. With no incentives, the proportion of smokers trying to quit who are still
The survey included 194 young adults (ages 18 to 24 ) and 53 of them said that they had used online dating. If we use this sample to estimate the proportion of all young adults to use online dating,
55- to 64-year-olds The survey included 411 adults between the ages of 55 and 64 , and 50 of them said that they had used online dating. If we use this sample to estimate the proportion of all
College-Educated or Not? The survey also asked participants for their level of education, and we wish to estimate the difference in the proportion to use online dating between those with a college
Comparing Males to Females In the survey, \(17 \%\) of the men said they had used online dating, while \(14 \%\) of the women said they had.(a) Find a \(99 \%\) confidence interval for the difference
The Lady Tasting Tea By some accounts, the first formal hypothesis test to use statistics involved the claim of a lady tasting tea. In the 1920 's Muriel Bristol-Roach, a British biological
The null and alternative hypotheses for a test are given as well as some information about the actual sample(s) and the statistic that is computed for each randomization sample. Indicate where the
Exercise 4.71 discusses a study comparing average brain size between three groups of subjects. In this exercise, we test for evidence that average brain size is larger in football players who have
Exercise 4.29 introduces a historical scenario in which a British woman, Muriel Bristol-Roach, claimed to be able to tell whether milk had been poured into a cup before or after the tea. An
Numerous studies have shown that a high fat diet can have a negative effect on a child's health. A new study suggests that a high fat diet early in life might also have a significant effect on memory
In a test to see whether males, on average, have bigger noses than females, the study indicates that " \(p
In a test to see whether there is a difference between males and females in average nasal tip angle, the study indicates that " \(p>0.05\)."Introduces a study examining whether or not noses continue
In a test to see whether there is a positive linear relationship between age and nose size, the study indicates that " \(p
If something costs more, do our expectations lead us to believe it is better? Because expectations play such a large role in reality, can a product that costs more (but is in reality identical)
In Exercise 4.16 we describe an observational study investigating a possible relationship between exposure to organophosphate pesticides as measured in urinary metabolites (DAP) and diagnosis of ADHD
Exercise 4.17 discusses an experiment done in Africa testing possible ways to reduce the spread of malaria by mosquitoes. In the experiment, 43 volunteers were randomly assigned to consume either a
If lizards adapt their behavior to the fire ants, then lizards from the invaded habitats should flee from the fire ants faster than lizards from the uninvaded habitats. Test this hypothesis. The
If lizards adapt their behavior to the fire ants, then lizards from the invaded habitats should twitch more than lizards from uninvaded habitats when exposed to red imported fire ants (twitching
Exercise 2.153 describes a study to compare the cost of restaurant meals when people pay individually versus splitting the bill as a group. In the experiment 48 subjects were randomly assigned to
Could owning a cat as a child be related to mental illness later in life? Toxoplasmosis is a disease transmitted primarily through contact with cat feces, and has recently been linked with
Testing \(H_{0}: p=0.5\) vs \(H_{a}: p>0.5\) using \(\hat{p}=0.55\) with each of the following sample sizes:(a) \(\hat{p}=55 / 100=0.55\)(b) \(\hat{p}=275 / 500=0.55\)(c) \(\hat{p}=550 /
Testing \(H_{0}: p=0.5\) vs \(H_{a}: p>0.5\) using \(\hat{p}=0.58\) with each of the following sample sizes:(a) \(\hat{p}=29 / 50=0.58\)(b) \(\hat{p}=290 / 500=0.58\)The same sample statistic is used
Testing \(H_{0}: p_{1}=p_{2}\) vs \(H_{a}: p_{1}>p_{2}\) using \(\hat{p}_{1}-\hat{p}_{2}=0.8-0.7=0.10\) with each of the following sample sizes:(a) \(\hat{p}_{1}=24 / 30=0.8\) and \(\hat{p}_{2}=14 /
Testing \(H_{0}: p_{1}=p_{2}\) vs \(H_{a}: p_{1}>p_{2}\) using \(\hat{p}_{1}-\hat{p}_{2}=0.45-0.30=0.15\) with each of the following sample sizes:(a) \(\hat{p}_{1}=9 / 20=0.45\) and \(\hat{p}_{2}=6 /
100 tests conducted using a significance level of \(5 \%\).We are conducting many hypothesis tests to test a claim. In every case, assume that the null hypothesis is true. Approximately how many of
300 tests using a significance level of \(1 \%\).We are conducting many hypothesis tests to test a claim. In every case, assume that the null hypothesis is true. Approximately how many of the tests
40 tests using a significance level of \(10 \%\).We are conducting many hypothesis tests to test a claim. In every case, assume that the null hypothesis is true. Approximately how many of the tests
800 tests using a significance level of \(5 \%\).We are conducting many hypothesis tests to test a claim. In every case, assume that the null hypothesis is true. Approximately how many of the tests
In Exercise 4.115, we compared the average difference between actual and scheduled arrival times for December flights on two major airlines: Delta and United. Suppose now that we are only interested
Exercise 4.119 on page 303 revealed an association between owning a cat as a child and developing schizophrenia later in life. Many people enjoy cats as pets, so this conclusion has profound
Exercise 4.119 on page 303 revealed an association between owning a cat as a child and developing schizophrenia later in life. Many people enjoy cats as pets, so this conclusion has profound
Does the ability to choose a mate improve offspring fitness in fruit flies? Researchers have studied this by taking female fruit flies and randomly dividing them into two groups; one group is put
Exercise 4.153 explores the question of whether mate choice improves offspring fitness in fruit flies, and describes two seemingly identical experiments yielding conflicting results (one significant,
Approval Rating for Congress In a Gallup poll conducted in December 2015, a random sample of \(n=824\) American adults were asked "Do you approve or disapprove of the way Congress is handling its
Correlation between points and penalty minutes for all 24 players with at least 10 games played for the 2014-2015 Ottawa Senators NHL hockey team. The data are given in Table 3.4 and the full data
Correlation between height and weight for players on the 2014 Brazil World Cup Team, using data from all 23 players on the roster. State whether the quantity described is a parameter or a statistic
Proportion of US adults who own a cell phone. In a survey of 1006 US adults in 2014, 90% said they had a cell phone. Give the correct notation for the quantity described and give its value.
In March 2015, a Nielsen global online survey "found that consumers are increasingly willing to pay more for socially responsible products." Over 30,000 people in 60 countries were polled about their
Data 2.7 on page 95 introduces the dataset HollywoodMovies, which contains information on more than 900 movies that came out of Hollywood between 2007 and 2013. One of the variables is the budget (in
One of the many wonderful things about studying statistics is that graduate programs in statistics often pay their graduate students, which means that many graduate students in statistics are able to
The dataset NFLContracts 2015 contains the yearly salary (in millions of dollars) from the contracts of all players on a National Football League (NFL) roster at the start of the 2015 season. (a)
Exercise 3.31 introduced the dataset StatisticsPhD, which gives enrollment for all 82 graduate statistics programs in the US in 2009. Use StatKey or other technology to generate a sampling
A Sampling Distribution for Average Salary of NFL Players Use StatKey or other technology to generate a sampling distribution of sample means using a sample of size \(n=5\) from the YearlySalary
Data 2.7 on page 95 introduces the dataset HollywoodMovies, which contains information on more than 900 movies that came out of Hollywood between 2007 and 2013. We will consider this the population
In Example 3.1, we see that \(27.5 \%\) of US adults are college graduates.(a) Use StatKey or other technology to generate a sampling distribution for the sample proportion of college graduates using
Gender in the Rock and Roll Hall of Fame From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals. Forty-seven of the inductees have been female or have
Performers in the Rock and Roll Hall of Fame From its founding through 2015, the Rock and Roll Hall of Fame has inducted 303 groups or individuals, and 206 of the inductees have been performers while
A Sampling Distribution for Gender in the Rock and Roll Hall of Fame Exercise 3.37 tells us that 47 of the 303 inductees to the Rock and Roll Hall of Fame have been female or have included female
Exercise 3.38 tells us that 206 of the 303 inductees to the Rock and Roll Hall of Fame have been performers. The data are given in Rock-and-Roll. Using all inductees as your population:(a) Use
Researchers continue to find evidence that brains of adolescents behave quite differently than either brains of adults or brains of children. In particular, adolescents seem to hold on more strongly
"For many people, being left alone with their thoughts is a most undesirable activity," says a psychologist involved in a study examining reactions to solitude. In the study, 146 college students
Exercise 3.58 describes a study in which college students found it unpleasant to sit alone and think. The same article describes a second study in which college students appear to prefer receiving an
Throughout the US presidential election of 2016, polls gave regular updates on the sample proportion supporting each candidate and the margin of error for the estimates. This attempt to predict the
Exercise 2.143 introduces a study examining the relationship between football playing and hippocampal volume, in \(\mu \mathrm{L}\), in the brain. We use the \(n=25\) participants in the control
For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles. The difference between these two values
The data in CarDepreciation given in Exercise 3.93 contains information on both New price and Depreciation for a sample of 20 automobile models.(a) Find the correlation between New price and
A study was conducted to investigate the relationship between severe headaches and being left- or right-handed. (Incidentally, Lisa Kudrow, who played Phoebe Buffay on the hit sitcom "Friends," is an
Use the closeness ratings before the activity (CloseBefore) to estimate the mean closeness rating one person would assign to others in a group.Use data from a study designed to examine the effect of
Use the closeness ratings given after the activity (CloseAfter) to estimate the difference in mean rating of closeness between those who have just done a synchronized activity and those who do a
Use the pain tolerance ratings (PainTolerance) after the activity to estimate the difference in mean pain tolerance between those who just completed a synchronized activity and those who did a
Use the pain tolerance ratings after the activity to estimate the difference in mean pain tolerance between those who just completed a high exertion activity and those who completed a low exertion
We see that 75 of the 264 people in the study allowed the pressure to reach its maximum level of \(300 \mathrm{mmHg}\), without ever saying that the pain was too much (MaxPressure=yes). Use this
The study recorded whether participants were female or male \((S e x=F\) or M), and we see that 33 of the 165 females and 42 of the 99 males allowed the pressure to reach its maximum level of \(300
Table 3.4 on page 208 shows the number of points scored and penalty minutes for 24 ice hockey players on the Ottawa Senators NHL team for the 2014-2015 season. The data are also stored in
We first study 3-PBA, a commonly used insecticide found in grains, fruits, and vegetables. How much higher are 3-PBA concentrations while not eating organic versus eating organic? A bootstrap
This is actually a paired data situation (since each person was measured before and after eating organic), so we create a new variable, the differences in pesticide concentration, by taking pesticide
You should have found that the confidence interval when utilizing the paired structure of the data was narrower than the confidence interval ignoring this structure (this will generally be the case,
In addition to the quantitative variable pesticide concentration, the researchers also report whether or not the pesticide was detected in the urine (at standard detection levels). Before the
There is some evidence that "young blood" might improve the health, both physically and cognitively, of elderly people (or mice). Exercise 2.69 on page 75 introduces one study in which old mice were
Of all 1,672,395 members of the high school class of 2014 who took the SAT (Scholastic Aptitude Test), 793,986 were minority students. Give the relevant proportion using correct notation.
Sports-Related Concussions in Kids Researchers examined all sports-related concussions reported to an emergency room for children ages 5 to 18 in the United States over the course of one year. Table
Culture and Mental Illness A recent study examining the link between schizophrenia and culture interviewed 60 people who had been diagnosed with schizophrenia and who heard voices in their heads. The
Help for Insomniacs In Exercise 1.23, we learned of a study to determine whether just one session of cognitive behavioral therapy can help people with insomnia. In the study, forty people who had
Success at Quitting Smoking After six months, 156 of the 914 smokers who accepted the invitation to be in the reward-only program stopped smoking, while 78 of the 146 smokers who paid a deposit quit.
Accounting for Participation Rates Exercises 2.30 and 2.31 show that smokers who agreed to be in the Deposit group (having their own money at risk) were much more likely to quit smoking than those
Class Year in Statistics The StudentSurvey data file contains information from a survey done the first day of an introductory statistics course. The Year variable shows the class year (FirstYear,
Bistro Servers The RestaurantTips data file comes from a sample of 157 bills at a small bistro/wine bar. Three different servers (labeled A, $\mathrm{B}$, and $\mathrm{C}$ ) worked on the nights the
Class Year by Gender Exercise 2.35 deals with the distribution of class Year for students in an introductory statistics course. The StudentSurvey data also has information on the Gender for each
Credit Card by Server The RestaurantTips data in Exercise 2.36 also has information on whether each bill was paid with a credit card or cash $($ Credit $=\mathrm{y}$ or $\mathrm{n})$. Use technology
Use technology and the data in StudentSurvey to construct a graph of the relationship between class Year and Gender for the situation in Exercise 2.37.Data From Exercise 2.37:Class Year by Gender
Use technology and the data in RestaurantTips to construct a graph of the relationship between Server and Credit for the situation in Exercise 2.38.Data From Exercise 2.38:Credit Card by Server The
Donating Blood to Grandma? Can young blood help old brains? Several studies in mice indicate that it might. In the studies, old mice (equivalent to about a 70-year-old person) were randomly assigned
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