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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

Heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches. a. What is the probability that a randomly
In Exercise 11.5.17 the instructor divided all the scores by 2 and then subtracted 1 point from each. Suppose a second method is to first subtract 1 from the scores and then divide by 2. a. How
Use the table in Exercise 11.2.18 on the distribution of students to answer the following questions. a. What proportion of all students are male? b. What proportion of all students are both
The NPR show Wait Wait ... Don’t Tell Me gives its guests a three-question quiz in which they have three answer choices for each question. The questions are so obscure that the guest typically must
Unfinished game: Suppose that Heather and Tom play a game that involves a series of coin flips. They agree that if 5 heads occur before 5 tails do, then Heather wins the game. But if 5 tails occur
Reconsider Exercise 11.1.19. a. Describe how you could use a simulation analysis to approximate the probability that Heather would win the game if it were finished. b. Use the following
It is estimated that 42% of all Americans have type A blood. Suppose two Americans are randomly selected (so the probability of one having type A blood is independent of the other). Find the
In 1938 Dr. Frank Benford, a physicist at General Electric, noticed that, given a list of numbers, more numbers started with the digit 1 than any other digit. He analyzed 20,222 sets of numbers
Recall Exercise 11.6.17 about getting into the New York City Marathon. You plan to enter until you get in and then won’t apply again. What is the smallest number of times you would have to enter so
The heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches and the heights of males are approximately
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. a. What is the probability that a randomly chosen
A sample of 65 healthy males in a vaccine trial had a mean body temperature of 98.105° Fahrenheit with a standard deviation of 0.699° Fahrenheit. If all these temperatures were converted to degrees
In Exercise 11.3.19 we saw that 42% of all Americans have type A blood. Assume five Americans are chosen at random. a. What is the probability that all of them have type A blood?b. What is the
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. The wheel is spun and a ball will
According to the Kaiser Family Foundation, the proportions of the U.S. population who have various types of health insurance in 2015 are as shown in the table a. Find the proportion of people
In a bone density test, one of the results is given as a z-score. This is simply the number of standard deviations above or below the average bone density of someone of the same sex and age as the
To answer the following questions, we assume the probability that a family has a boy or a girl is the same (0.50) and that a family will have three children. a. Write out the sample space by
Are metal bands used for tagging harmful to penguins? In Nature, researchers Saraux et al. reported the results of an investigation done to answer this question using a sample of 100 penguins near
A sample of 65 healthy females in a vaccine trial had a mean body temperature of 98.394° Fahrenheit with a standard deviation of 0.743° Fahrenheit. If all these temperatures were converted to
Suppose that a basketball player named Jose makes 60% of his free throws, and Kayla makes 70% of her free throws. Each player attempts 100 free throws at the end of practice one day. Regard these as
Reconsider the Exercises 11.1.19 and 11.1.20. a. Suppose that the rules were changed so that the winner is the first to reach 10 heads or tails, rather than 5. (Continue to assume that the game
A string of cheap Christmas lights contains 10 lights. Each individual light has a 0.10 probability of failing during the Christmas season. Assume the lights fail independently of each other. a.
Reconsider the roulette wheel description in Exercise 11.6.20. If you bet $1 on red and the ball lands on a red number, you will get your $1 back plus another $1. If the ball does not land on a red
Reconsider Exercise 11.8.20. Describe how the probability that ((p(vector)Kayla − p(vector)Jose > 0) would change if: a. The sample sizes were larger. b. Kayla’s probability of
Suppose two parents have blood genotypes such that the probability that any of their children have blood type A is 0.75. a. If they have 5 children: i. What is the probability that all have
Suppose that Karen and John get together to grade their students’ exams. The time required for Karen to grade a question on a student’s exam is normally distributed with mean 90 seconds and
According to a study done in the United Kingdom, a male’s probability of death from lung cancer during his lifetime is 0.077. For someone that is a heavy smoker (at least 25 cigarettes a day), that
The two distributions for Exercise 2.2.14 are the mean length of words from samples of 10 words and 30 words from the Gettysburg Address. Which distribution comes from samples of size 10 and which
Recall Exercise 3.4.41 about the size of a sample needed for a margin of error of at most 0.03. What sample size is needed to have a margin of error of at most 0.03 for a 99% confidence interval? Use
You often see margins of errors in polling results listed as ±3%. What sample size do you need to have a margin of error of at most 0.03 for a 95% confidence interval? To answer this question, set
Refer to Exercise 8.2.25 on accuracy in surveys. Another way to measure accuracy of responses is whether people round when giving numerical answers. The researchers considered a number to be rounded
Data were gathered on 106 statistics students from a Midwestern college on variables including the sex of the respondent and whether they had eaten breakfast that morning.If there were no association
What are the observational units?Social psychologists throughout the years have shown that an aggression–sexuality link exists not only in various animal species but also in humans. Dutton and Aron
Recall Exercise 7.3.34 about comparing ratings of intensity for male-named hurricanes and female-named hurricanes. a. Put the data into the Matched Pairs applet to find the sample mean, sample
Reconsider Exercises 8.1.23–8.1.25 on cell phone and smartphone ownership. We considered our population to be that of all adults in the United States. Now suppose we want the population to be all
Two samples of Facebook users chosen by the Pew Research Center (one in 2019 and one in 2013) were asked how often they visit or use Facebook. The results are shown in the two-way table. We will
Bergmann’s rule (named after German biologist Carl Bergmann) is an ecogeographical rule that states that within a species, specimens will tend to be larger if they are from cooler climates or more
Given the information in this partial ANOVA table, what is the value of the F-statistic? A. 0.76 B. 2.31 C. 7.59 D. 10.02 E. 17.53 Source
Two researchers (Veronica and Bella) are working separately to investigate whether reaction time (seconds) is associated with the presence and type of music that is playing in the background. Summary
When surveys are administered, it is hoped that the respondents give accurate answers. Does the mode of survey delivery affect this? American researchers investigated this question (Schober et al.,
Recall Exercise 8.1.30 on accuracy of survey responses. Another way to measure accuracy of responses is whether people round when giving numerical answers. The researchers considered a number to be
Recall that two researchers (Veronica and Bella, in Exercise 9.1.4) are working separately to investigate whether reaction time (seconds) is associated with the presence and type of music that is
Recall that two researchers (Veronica and Bella, in Exercises 9.1.4 and 9.1.5) are working separately to investigate whether reaction time (seconds) is associated with the presence and type of music
When testing for an association between class level (Freshman, Sophomore, Junior, Senior) and IQ score, which of A–D is NOT an appropriate way to write the alternative hypothesis?A. There is an
Suppose you are comparing three groups with a quantitative response. You calculate an F-statistic and determine a p-value. Now suppose the standard deviations for your three groups increase, yet the
Which of A–D best describes the F-statistic? A. (Between-group variability)/(total variability) B. (Total variability)/(between-group variability) C. (Between-group
Which of the A–D are NOT validity conditions needed to use a theory-based F-distribution to determine a p-value? (Choose all that apply.) A. The sample sizes in each group must be the
When comparing multiple groups with a quantitative response using an ANOVA test, which conditions will decrease the p-value? (Choose all that apply.) A. Increasing the sample size for each
Does being told whether water is from the tap or bottled influence how people rate how good it tastes? Student researchers set out to answer this question. In a blind taste test, they asked 31
You are given the following regression output where the height of a person, in inches, is being used to predict the amount of sleep he or she gets per night, in hours. What is the value of the
Some breeds of dogs, like bloodhounds, have been bred to perform well on scent detection, and some breeds have not. So how do these different types of dogs compare on a scent detection test, and how
Some breeds of dogs, like bloodhounds, have been bred to perform well on scent detection, and some breeds have not. So how do these different types of dogs compare on a scent detection test, and how
Use the scatterplot below to answer these questions. a. Which labeled point or points have positive residuals? b. Which labeled point or points have negative residuals? c. Which
Which answer best describes the direction, form, and strength of the association between physical warmth (Temp) as measured by oral temperature in degrees Celsius and social warmth as measured by a
Which answer best describes the direction, form, and strength of the association between the distance of a hike (in miles) and the time it takes to complete the hike (in minutes). A. Positive,
You are given the following regression output, where the height of a person, in inches, is being used to predict the amount that person sleeps per night, in hours. What is the equation of the
In conducting a simulation using cards to test for the linear association between two quantitative variables, cards that have the values of the response variable are shuffled and then: A. Put in
A residual is calculated by using which of the following? A. ŷ − y B. y − ŷC. ŷ − x D. x − ŷE. x − x̂
When testing to see whether there is an association between two quantitative variables, what statistic can we use? A. The difference in the means between the two variables B. The Mean Group
The null distribution used to test to see whether there is an association between two quantitative variables consists of simulated: A. Correlations. B. Mean Group Diff statistics. C.
College students were asked how many classes they failed to attend in the past 3 weeks as well as their current grade point average. We obtained the following regression equation from the resulting
It is said that if someone is more left-brained they are more analytical and verbal, whereas a more right-brained person is more visual and intuitive. Student researchers used an 30-second online
What number do we calculate to tell us whether there is a strong linear association between two quantitative variables, and what number do we calculate to tell us whether there is strong evidence of
Which of these is NOT one of the validity conditions for a t-test for the slope of a regression line? A. We should have a large sample size, typically n ≥ 20. B. The scatterplot of the
Match the correct scatterplot number from the Exercise 10.1.9 plots to the correlation coefficient. a. r = 0.754 ______ b. r = 0.176 ______ c. r = –0.439 ______ d. r =
Which of the following correlation coefficients shows the strongest linear association? A. 0.689 B. 0.302 C. 0.001 D. –0.736
Match the correct scatterplot number from the Exercise 10.1.10 plots to the correlation coefficient. a. r = 0.739 ______ b. r = 0.323 ______ c. r = –0.742 ______ d. r = –0.937
When we complete a test for the slope of a regression line, which of these is an appropriate way to write the null hypothesis? A. H0: μ = 0 B. H0: π = 0 C. H0: β = 0 D.
Which of the following correlation coefficients shows the strongest positive linear association? A. 0.892 B. 0.411 C. 0.031 D. 0.005
Suppose we are conducting a two-sided t-test for the slope of a regression line where the null hypothesis is that there is no linear association between the explanatory and response variables, and we
Which of the following correlation coefficients shows the strongest negative linear association? A. –0.013 B. –0.066 C. –0.598 D. –0.912
A person who can identify or produce a musical tone correctly without any outside reference is said to have perfect pitch. This can be tested using a pitch identification test (PIT). Perfect pitch
Researchers in the journal Nature (Tatem et al., 2004) explored the winning times of the 100-meter dash in the Olympics for both men and women. Using the winning times in the 1900 to 2004 Olympics,
We want to predict the height of someone given their foot length. To do this, we obtained a random sample of 81 high school students who gave their height and foot length in centimeters. Software
Three statements about what you can learn from the correlation coefficient are listed in (a)–(c). Label each statement, choosing from A (can always tell), N (can never tell), or S (can sometimes
Reconsider Exercise 10.5.15 on age and BMI. a. Determine a 95% confidence interval for the population slope and interpret what this interval represents. b. Based on your confidence
It is said that if someone is more left-brained they are more analytical and verbal, whereas a more right-brained person is more visual and intuitive. Student researchers used an online 30-second
Fill in the blanks based on the patterns in the data. a. For restaurants, the correlation between average noise level and time becomes ________ (stronger/weaker) if you exclude the two
Glycemic load is a number that describes the quantity and quality of carbohydrates in food. For example, a muffin or a piece of cake has a very high glycemic load number, because each contains lots
A person who can identify or produce a musical tone correctly without any outside reference is said to have perfect pitch. This can be tested using a pitch identification test (PIT). Perfect pitch
Researchers at UCLA (Inagaki et al., 2016) investigated the relationship between physical warmth and social warmth. They measured physical warmth by taking oral temperatures of the 54 subjects (in
Some studies have suggested that aerobic activity can benefit brain development and cognition in growing children (Chaddock-Heyman, 2015). It is thought that the higher your aerobic activity as
The dataset HeightReactTime contains people’s height, in centimeters, and reaction time, in seconds, from a computer-based test from a sample of 48 U.S. high school students in 2019. Using slope as
In a survey of college statistics students, 78 females were asked what their height was and if they could magically be any height they wanted, what their magical height would be. Both of these
Refer to Exercise 10.CE.25 about VO2 max and the thickness of grey matter in the superior frontal lobe of the brain. A statistically significant negative linear association was found between these
Psychologists in many countries use children’s human figure drawings (Draw-A-Person Intellectual Ability Test, or DAPIQ) to assess intellectual ability. Basically, a child is asked to draw
The dataset HeightReactTime contains people’s height, in centimeters, and reaction time, in seconds, from a computer-based test from a sample of 48 U.S. high school students in 2019. We want to
Refer to Exercises 10.CE.25 and 10.CE.26 on VO2 max and cortical grey matter in the brain. The paper’s title, “The Role of Aerobic Fitness in Cortical Thickness and Mathematics Achievement in
In a survey of college statistics students, 78 females were asked what their height was and if they could magically be any height they wanted, what their magical height would be. Both of these
Recall Exercise 10.5.28 on body image and attention to detail. In addition using inverted faces to test the participants, the researchers tested their attention to detail with inverted clothed human
In a survey of 106 college students, data were gathered on the number of piercings each student had and the number of classes they had skipped in the past 3 weeks. We want to determine whether there
A random sample of 15 students from a database of U.S. high school students was taken. The data in the Exercise 10.2.30 table provide the height of each student and the width of their outstretched
Glycemic load is a number that describes the quantity and quality of carbohydrates in food. For example, a muffin or a piece of cake will have a very high glycemic load number because each contains
In 2015, we sampled 13 homes from Zillow that were for sale just north of a small lake in Michigan and recorded the selling price and the square footage of the home. The results are shown in the
In a survey of college students, data were gathered on their actual height (height) in inches and the height they would like to be if they could magically be any height (magic height). The results,
In 2015, we sampled 13 homes from Zillow that were for sale just north of a small lake in Michigan and recorded the selling price and the square footage of the home. The results, shown in the
Temperature affects the rate at which a cricket chirps; the higher the temperature, the faster the rate. A South African researcher collected data (chirp rate in chirps per second and air temperature
In a survey of college students, data were gathered on their actual height (height) in inches and the height they would like to be if they could magically be any height (magical height). The results,
Temperature affects the rate at which a cricket chirps; the higher the temperture, the faster the rate. A South African researcher collected data (chirp rate in chirps per second and air temperature
Body image concern ranges from a healthy and positive body image to a mental illness involving obsessive focus on a perceived flaw in appearance. Researchers (Beilharz et al., 2016) measured body

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