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mathematics
statistics the art and science
Questions and Answers of
Statistics The Art and Science
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the two
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the two
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the two
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the two
Two sets of sample data, A and B, are given. Without doing any calculations, indicate in which set of sample data, A or B, there is likely to be stronger evidence of a difference in the two
In another study to investigate the effect of women’s tears on men, 16 men watch an erotic movie and then half sniff women’s tears and half sniff a salt solution while brain activity is
To study the effect of women’s tears on men, levels of testosterone are measured in 50 men after they sniff women’s tears and after they sniff a salt solution. The order of the two treatments was
Data 2.11 on page 111 introduces the dataset NutritionStudy which contains, among other things, information about smoking history and gender of the participants. Is there a significant association
Data 2.11 on page 111 introduces the dataset NutritionStudy which contains, among other things, information about vitamin use and gender of the participants. Is there a significant association
Exercise 7.41 on page 485 describes an experiment on helping cocaine addicts break the cocaine addiction, in which cocaine addicts were randomized to take desipramine, lithium, or a placebo. The
We see in the previous two exercises that sprinters are more likely to have allele R and genotype RR versions of the ACTN3 gene, which makes these versions associated with fast-twitch muscles. Is
The study on genetics and fast-twitch muscles includes a sample of elite sprinters, a sample of elite endurance athletes, and a control group of nonathletes. Is there an association between genetic
The study on genetics and fast-twitch muscles includes a sample of elite sprinters, a sample of elite endurance athletes, and a control group of nonathletes. Is there an association between genotype
Exercise 7.45 introduced a 2010 study about users of social networking sites such as Facebook. Table 7.34 shows the frequency of users liking content on Facebook,
Exercise 7.45 introduced a 2010 study about users of social networking sites such as Facebook. Table 7.33 shows the self-reported frequency of status updates on Facebook by gender. Are frequency of
Exercise 7.45 introduced a 2010 study about users of social networking sites such as Facebook. Table 7.32 shows the self-reported frequency of status updates on Facebook by age groups.Table 7.32(a)
The Pew Research Center conducted a survey of randomly sampled American adults in 2008 and in 2010, asking them about their use of social networking sites such as Facebook. Table 7.31 shows age
Is the career someone chooses associated with being left- or right-handed? In one study a sample of Americans from a variety of professions were asked if they consider themselves left-handed,
Exercise 7.13 on page 472 discusses a sample of people choosing their favorite Skittles flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 91 people, again asking them
Throughout Unit C we examined various relationships between the variables regarding houses for sale in the dataset HomesFor- Sale. One topic of repeated interest was differences between states. We
Cocaine addiction is very hard to break. Even among addicts trying hard to break the addiction, relapse is common. (A relapse is when a person trying to break out of the addiction fails and uses
In Exercise 6.178 on page 403 we perform a test for the difference in the proportion of penguins who survive over a 10-year period, between penguins tagged with metal tags and those tagged with
In Data 2.1 on page 46, we introduce a study in which people were asked whether they agreed or disagreed with the statement that there is only one true love for each person. Table 7.27 gives a
Example 2.6 on page 51 contains a two-way table showing preferences for an award (Academy Award, Nobel Prize, Olympic gold medal) by gender for the students sampled in StudentSurvey. The data are
Two-way table in Exercise 7.30(Group 3, Yes) cellRefer to the tables in Skill Builder 1. In each case, give the degrees of freedom for the chi-square test based on that two-way table. Yes No
Give a two-way table and specify a particular cell for that table. In each case find the expected count for that cell and the contribution to the chi-square statistic for that cell.(Group 2, No) cell
Give a two-way table and specify a particular cell for that table. In each case find the expected count for that cell and the contribution to the chi-square statistic for that cell.(Control,
Give a two-way table and specify a particular cell for that table. In each case find the expected count for that cell and the contribution to the chi-square statistic for that cell.(B, E) cell Total
Give a two-way table and specify a particular cell for that table. In each case find the expected count for that cell and the contribution to the chi-square statistic for that cell.(Group 3, Yes)
Refer to the data in Digits that are described in Exercise 7.28. The 150 students were also asked to give the last two digits of their nine-digit social security number. Those digits are stored in
How well can people generate random numbers? A sample of students were asked to write down a ‘‘random” four-digit number. Responses from 150 students are stored in the file Digits. The data
The game of craps is a gambling game where players place wagers on the sum from the roll of two six-sided dice. One author rolled a pair of dice 180 times and recorded the results in Table 7.18. He
Refer to the discussion of Benfords law in Exercise 7.25. While this may seem like a curious oddity, researchers have developed some important applications for these proportions. One
Frank Benford, a physicist working in the 1930s, discovered an interesting fact about some sets of numbers. While you might expect the first digits of numbers such as street addresses or checkbook
Exercise 7.23 discusses a study investigating the ACTN3 genotypes RR, RX, and XX. The same study also examines the ACTN3 genetic alleles R and X, also associated with fast-twitch muscles. Of the 436
Chisquare tests are common in genetics. A gene called ACTN3 encodes a protein which functions in fasttwitch muscles. People have different variants of this gene, classified as RR, RX, or XX. Computer
Major League Baseball is split into six divisions, one of which is the American League West. While specific teams in each division change often, the four teams currently in the AL West have been
Movies based on Ian Fleming’s novels starring British secret agent James Bond have become one of the longest running film series to date. Over the course of the series, six different actors have
A new study indicates that elderly people are able to postpone death for a short time to reach an important occasion. The researchers studied deaths from natural causes among 1200 elderly people of
Assume you are working as a statistician for the automotive company Ford. Ford’s three most popular cars are the Escape (SUV), the Focus (midsize sedan), and the Fusion (hybrid sedan). Your boss is
Most medical school graduates in the US enter their residency programs at teaching hospitals in July. A recent study suggests that a spike in deaths due to medication errors coincides with this
Most Australian youth-sports leagues separate athletes by birthdate, and the cutoff date is January 1st. Thus, those children born in January and February have some physical advantages in youth
In his book Outliers: The Story of Success (2008), Malcolm Gladwell speculates that Canadian ice hockey players that are born early in the year have an advantage. This is because the birthdate cutoff
As recently as 2008, 70% of users of social networking sites such as Facebook were 35 years old or younger. Now the age distribution is much more spread out. Table 7.10 shows the age distribution of
In Data 6.1 on page 367 we see a table, reproduced in Table 7.9, that shows the choices made by 119 players on the first turn of a Rock-Paper-Scissors game. Recall that rock beats scissors which
Skittles are a popular fruity candy with five different flavors (colored green, orange, purple, red, and yellow). A sample of 66 people recorded their favorite flavor and the results are shown in
Give a null hypothesis for a goodness-of-fit test and a frequency table from a sample. For each table, find:(a) The expected count for the category labeled B(b) The contribution to the sum of the
Give a null hypothesis for a goodness-of-fit test and a frequency table from a sample. For each table, find:(a) The expected count for the category labeled B(b) The contribution to the sum of the
Give a null hypothesis for a goodness-of-fit test and a frequency table from a sample. For each table, find:(a) The expected count for the category labeled B(b) The contribution to the sum of the
Give a null hypothesis for a goodness-of-fit test and a frequency table from a sample. For each table, find:(a) The expected count for the category labeled B(b) The contribution to the sum of the
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the Ï2-test
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the Ï2-test
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the Ï2-test
The categories of a categorical variable are given along with the observed counts from a sample. The expected counts from a null hypothesis are given in parentheses. Compute the Ï2-test
Find the expected counts in each category using the given sample size and null hypothesis.H0: p1 = 0.7, p2 = 0.1, p3 = 0.1, p4 = 0.1; n = 400
Find the expected counts in each category using the given sample size and null hypothesis.H0: pA = 0.50, pB = 0.25, pC = 0.25; n = 200
Find the expected counts in each category using the given sample size and null hypothesis.H0 All three categories A, B, C are equally likely; n = 1200
Find the expected counts in each category using the given sample size and null hypothesis.H0: p1 = p2 = p3 = p4 = 0.25; n = 500
To study the effect of sitting with a laptop computer on one’s lap on scrotal temperature, 29 men have their scrotal temperature tested before and then after sitting with a laptop for one hour.A
Test H0: μA = μB vs Ha: μA ≠ μB using the fact that Group A has 8 cases with a mean of 125 and a standard deviation of 18 while Group B has 15 cases with a mean of 118 and a standard deviation
Test H0: μT = μC vs Ha: μT < μC using the fact that the treatment group (T) has a sample mean of 8.6 with a standard deviation of 4.1 while the control group (C) has a sample mean of 11.2 with
Do left-handed or right-handed people make more money? One study recorded the hourly earnings for a random sample of 2295 American men, of whom 2027 were right-handed and 268 were left-handed. The
Researchers randomly assigned 107 young over weight women to cut 25% of their calories in one of two ways: The continuous group ate about 1500 calories a day every day while the intermittent group
In 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters.” She recruited 75 female maids working in different hotels to participate in her study, and informed 41 maids
Many studies have shown that people who engage in any exercise have improved mental health over those that never exercise. In particular, even a small amount of exercise seems to confer some
Studies are finding that bacteria in the stomach are essential for healthy functioning of the human body. One study68 compared the number of unique bacterial genes in stomachs of healthy patients and
Exercise B.5 on page 305 introduces a study examining 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
Drinking tea appears to offer a strong boost to the immune system. In a study introduced in Exercise 3.82 on page 203, we see that production of interferon gamma, a molecule that fights bacteria,
Data 1.3 on page 10 discusses a study designed to test whether applying a metal tag is detrimental to a penguin, as opposed to applying an electronic tag. One variable examined is the length of
Data 1.3 on page 10 discusses a study designed to test whether applying a metal tag is detrimental to a penguin, as opposed to applying an electronic tag. One variable examined is the date penguins
In each case below, two sets of data are given for a two-tail difference in means test. In each case, which version gives a smaller p-value relative to the other?(a) Both options have the same
A statistics professor was handing out midterm grade slips on a Friday which happened to be the day before the schools Spring break. He noticed that there were an unusually large number
A young statistics professor decided to give a quiz in class every week. He was not sure if the quiz should occur at the beginning of class when the students are fresh or at the end of class when
The dataset ICU-Admissions contains information on a sample of 200 patients being admitted to the Intensive Care Unit (ICU) at a hospital. One of the variables is HeartRate and another is Status
Use technology and the StudentSurvey dataset to test whether the data provide evidence that there is a difference in the mean number of hours of exercise per week between males and females. What are
Use technology and the StudentSurvey dataset to test whether the data provide evidence that there is a difference in the mean number of hours spent watching television per week between males and
The data in CommuteAtlanta (see Data 3.3 on page 193 for more description) contain a variable that identifies the sex of each commuter in the Atlanta sample. Test at a 5% level whether there is a
A 95% confidence interval for μ1 − μ2 using the paired difference sample results x̅d = 3.7, sd = 2.1, nd = 30Use a t-distribution to find a confidence interval for the difference in means μ1
A 90% confidence interval for μ1 − μ2 using the paired difference sample results x̅d = 556.9, sd = 143.6, nd = 100Use a t-distribution to find a confidence interval for the difference in means
A 99% confidence interval for μ1 μ2using the paired data in the following table:Use a t-distribution to find a confidence interval for the difference in means
A 95% confidence interval for μ1 μ2using the paired data in the following table:Use a t-distribution to find a confidence interval for the difference in means
Test H0: μ1 = μ2 vs Ha: μ1 ≠ μ2 using the paired difference sample results x̅d = 15.7, sd = 12.2, nd = 25.Use a t-distribution and the given matched pair sample results to complete the test of
Test H0: μ1 = μ2 vs Ha: μ1 ≠ μ2 using the paired difference sample results x̅d = −2.6, sd = 4.1, nd = 18.Use a t-distribution and the given matched pair sample results to complete the test
Test H0: μ1= μ2vs Ha: μ1< μ2using the paired data in the following table:Use a t-distribution and the given matched pair sample results to
Test H0: μ1= μ2vs Ha: μ1> μ2using the paired data in the following table:Use a t-distribution and the given matched pair sample results to
In a study to determine whether the color red increases how attractive men find women, one group of men rate the attractiveness of a woman after seeing her picture on a red background and another
A study investigating the effect of exercise on brain activity recruits sets of identical twins in middle age, in which one twin is randomly assigned to engage in regular exercise and the other
We saw in Exercise 6.260 on page 425 that drinking tea appears to offer a strong boost to the immune system. In a study extending the results of the study described in that exercise, blood samples
Exercise 4.86 on page 263 introduces a matched pairs study in which 47 participants had cell phones put on their ears and then had their brain glucose metabolism (a measure of brain activity)
Exercise 6.284 describes a study to examine the effects of tea on the immune system. Use the information there to test whether mean production of interferon gamma as a response to bacteria is
Exercise 6.285 describes a matched pairs study examining the effect of cell phones on brain glucose metabolism. Use the information there to test to see if there is evidence that mean glucose
On page 11 in Section 1.1, we describe studies to investigate whether there is evidence of pheromones (subconscious chemical signals) in female tears that affect sexual arousal in men. In one of the
Exercise 6.288 describes a study to measure, in a doubleblind randomized experiment, the effect of female tears on male testosterone. Use the information there to find a 99% confidence interval for
Do you think your pulse rate is higher when you are taking a quiz than when you are sitting in a lecture? The data in Table 6.27 show pulse rates collected from 10 students in a class lecture and
Exercise 6.290 describes pulse rates collected from 10 students, once during a quiz and once during a lecture. The data are given in Table 6.27 and stored in QuizPulse10. We might expect mean pulse
A story spoiler gives away the ending early. Does having a story spoiled in this way diminish suspense and hurt enjoyment? A study investigated this question. For 12 different short stories, the
Exercise 6.292 describes a study investigating whether giving away the ending of the story makes the story more or less enjoyable to read. The data are given in Table 6.28 and stored in
How big is the home field advantage in the National Football League (NFL)? In Exercise 6.240 on page 419, we examine a difference in means between home and away teams using two separate samples of 80
Table 6.29 gives a sample of grades on the first two quizzes in an introductory statistics course. We are interested in testing whether the mean grade on the second quiz is significantly higher than
Test H0: μ1 = μ2 vs Ha: μ1 ≠ μ2 using the sample results x̅1 = 15.3, s1 = 11.6 with n1 = 100 and x̅2 = 18.4, s2 = 14.3 with n2 = 80.Use the t-distribution and the given sample results to
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