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introduction to statistical investigations
Questions and Answers of
Introduction To Statistical Investigations
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
Consider the question of whether sick days in a company are equally likely to occur Monday through Friday. a. State the null and alternative hypotheses using symbols. b. If we conduct a
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.,
In a January 2019 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a cell phone. The results are shown in the following table by race. a. What
In a January 2019 poll conducted by the Pew Research Center, they asked a random sample of U.S. adults if they owned a smartphone. The results are shown in the following table by race.a. What
Reconsider Exercise 8.1.23 on cell phone use. Complete a test of significance to determine if there is an association between race and whether someone owns a cell phone using p?max − p?min as the
A study done in Germany (Willich et al., 1993) looked at which days of the week people had heart attacks. One subgroup the researchers looked at were those who were employed. They found that the 884
Researchers in Brazil explored the relationship between overconfidence and accuracy among Brazilian accountants (Cardoso, 2016). Based on a presurvey, the researchers classified their subjects as
Recall the study in Exercise 8.3.21 on which days of the week people experienced heart attacks. Another subgroup the researchers looked at were those who were not employed. They found that the 1,191
Does the color of a sign that asks someone to do something make a difference in a person’s obedience to that sign? This is what a student researcher investigated. There are double doors at the
In one set of Mendel’s pea experiments, he crossed a round-green pea with a wrinkled-yellow pea (Mendel, 1866). The result of this cross gave him a round-yellow pea. He then crossed two of these
In Exercise 8.1.21 about cell phone use, what if the question was “Are students more likely to be on their cell phones in the evening as they walk across campus than during the daytime?” How
Mendel took the 315 seeds from the round-yellow peas he obtained from the experiment given in Exercise 8.3.16 and planted them. Fourteen of the plants did not grow or did not produce seeds. Of the
Are college students more likely to be on their cell phone at certain times of day than other times as they walk across their campus? Student researchers explored this question. Of the 221 students
Recall Exercise 8.3.19 about dialysis patients dying of heart attacks. The researchers also looked at patients that had their dialysis done on Tuesday, Thursday, and Saturday and experienced cardiac
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
In another set of Mendel’s pea experiments, he crossed a purple-flowered pea plant with a white-flowered pea plant. This resulted in plants that were all purple-flowered. He then took these
One of the authors’ cell phones recently became able to state a random number when asked. The author wondered whether the phone’s method of picking a random number was truly random. He asked his
Student researchers asked 84 students whether they were willing to take a survey. Some of the students were offered an incentive of a candy bar and some were not. The summary of the results are
In addition to having dice pushed off a 2-inch ledge, as in the example in this section, the researchers also pushed dice off a 4-inch-high ledge with the following results.Is this an unfair way to
Recall Exercise 8.3.13 on commercial models and their eye colors. The researchers also explored the eye colors of registered commercial models in Brazil. They sampled from 400 profiles of females
Do female models have eye colors that are distributed differently than those of the population of their country? That is a question that UK researchers were interested in exploring (Forti, 2016).
A random sample of 100 high school students was taken and the following table gives a summary of their responses when they were asked what their favorite season is. We are interested in testing to
Calculate the chi-square test statistic for the following datasets and null hypotheses. a. H0: πA = πB = πC = 1.3 b. H0: πA = πB = πC = 1.3 Observed count Category A B C 12 16
Consider doing a chi-square goodness-of-fit test with the null hypothesis of π1 = π2 = π3 = 1/3 on two different sets of data. For categories 1, 2, and 3, respectively, dataset A has observed
What data type is used in a chi-square goodness-of-fit test? How does that compare with the type of data used in the type of chi-square test you did in Section 8.2?
Calculate the chi-square test statistic for the following datasets and null hypotheses a. H0: The population is distributed in a ratio of 1:2:1 for the categories A, B, and C, respectively.b.
The following distributions represent colors of 100 candies. You want to run a chi-square goodness-of-fit test with the null hypothesis that the distribution of colors is evenly distributed. Which of
In running a chi-square test of significance on the data from the graph in Exercise 8.2.3 about comparing coffee drinking between where students live, which of A-E is the appropriate way to write the
State the null and alternative hypotheses to be investigated with this study. (You may use the symbol π to represent these parameters.) The following table provides descriptive statistics on the 152
Suppose you complete a chi-square test to see whether there is a difference in the proportion of Republicans, Democrats, and Independents that favor a new law and get a p-value of 0.01. You then
The summarized data from a survey of college students, in which they were asked where they live (Dorm, College apartment, or Off campus) and whether or not they regularly drink coffee are shown in
Using the data in the following table, what is the chi-square test statistic? A. 0.93 B. 4.93 C. 5.38 D. 8.13 E. 484.93 Category A B C D 39 20 Observed count 10 51 Expected
Suppose we are comparing three proportions using a chi-square test. If the data are adjusted so the proportions are farther apart (but the sample sizes stayed the same for each condition),
Recall Exercise 8.2.2 on where students live and whether they regularly drink coffee. The results of the survey are shown in the mosaic plot. Which of these would you predict to be the findings if a
College students were asked to rate their abilities as drivers and how often they text while driving, with the summarized data shown in the Exercise 8.2.1 table. Are validity conditions met for a
Suppose you are running a chi-square goodness-of-fit test on a dataset that has five categories and you calculate a chi-square test statistic of 7.46. What is the corresponding p-value? A.
Partial results of a survey of college students, in which they were asked where they live (dorm, college apartment, or off campus) and whether they regularly drink coffee are shown in the following
Which of A–E is the proper way to write out the alternative hypothesis for the test from Exercise 8.3.1 on candy flavor distribution? A. The long-run percentages of candies are distributed 50%
The flavors of a certain kind of candy are supposed to be distributed as follows: 50% cherry, 30% lemon, and 20% orange. You randomly sample 180 of these candies to run a chi-square goodness-of-fit
Completing a chi-square test on a 2 × 2 table is equivalent to what other type of test (with a two-sided alternative)? A. One-proportion z-test B. Two-proportion z-test C. One-sample
Seagulls are notorious for stealing food from people. Will staring at them be a deterrent? Researchers (Goumas et al., 2019) set French fries in a sealed plastic bag on the ground and then crouched
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