Stats exam
The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below. In this study, the explanatory variable is: the volume of oxygen consumed while running. the instrument used to measure the volume of oxygen consumed. the volume of oxygen consumed at rest. either variable—it doesn't matter which is considered the response.
c
A newspaper article is summarized: According to a new study, teachers may be more inclined to give higher grades to students, hoping to gain favor with the university administrators who grant tenure. The study examined the average grade and teaching evaluation in a large number of courses given in 1997 in order to investigate the effects of grade inflation on evaluations. "I am concerned with student evaluations because instruction has become a popularity contest for some teachers," said Professor Smith, who recently completed the study. Results showed higher grades directly corresponded to a more positive evaluation. Which of the following would be a valid conclusion to draw from the study? Higher grades result in above-average teaching evaluations. None of the answer options is correct. Teachers can improve their teaching evaluations by giving higher grades. A good teacher, as measured by teaching evaluations, helps students learn better, which results in higher grades.
b
A researcher states that bone density in women is negatively associated with age. This means that:below-average values of age tend to accompany below-average values of bone density.as women get older, bone density tends to decrease. as women get older, bone density tends to increase.older women aren't any more likely than younger women to have below-average bone density.
b
A survey of radio stations was conducted following the attacks on the World Trade Center in 2001 . The station rankings were included in the survey. The histogram below has the interval limits 0≤𝑋<50 , 50≤𝑋<100 , 100≤𝑋<150 , 150≤𝑋<200 , and 200≤𝑋<250 . A ranking of 100: a) cannot be determined from the histogram. b) will be counted in interval 3 c) can be in either interval 2 or 3 d) will be counted in interval 2
b
A survey of radio stations was conducted following the attacks on the World Trade Center in 2001. One of the variables recorded was the region the station was located in (east, center, or west). The bar chart above shows that the location of the majority of radio stations: is in the east. is in the center. cannot be determined from a bar chart. is in the west.
b
A teacher returns an exam with possible scores ranging from 0 to 100 . The students suspect that the majority of them performed poorly on the exam and request summary statistics. The teacher provides the mean, which was 72 , as a summary statistic. A total of 400 students took the exam. Some of the students find the mean to be high, based on talking to other students. They take a random sample of 15 students, and they find that the mean equals 71.5 while the median equals 62 . Based on this result, we conclude that: exam scores are likely right-skewed. All of the answer options are correct. 50% of the students barely managed to pass the exam. there are possibly some large outliers in these data.
b
The graph below shows the scores students in an advanced statistics course received for homework completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500 and the maximum midterm score was 350 . The mean homework score was 356 for the 10 students, and the mean exam score was 238 . If a student had scored exactly 356 on the homework and 238 on the midterm, the residual would be approximately: −1 . 1 . 0 . The answer cannot be determined with the information given.
c
A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4 . Out of the 163 people who made it through the interview process, only 121can be hired. What cut-off GPA should the company use? 3.00 3.12 3.08 3.04
d
A modified boxplot for a right-skewed data set uses a special character to point to: the third quartile. the median. the maximum. an outlier.
d
A scatterplot of the amount of alcohol consumed according to a food diary (DR) against the amount of alcohol consumed on a frequent food questionnaire (FFQ):shows the answers each study participant gave on the FFQ and the DR.assesses whether the relationship between the answers on the DR and the FFQ is positive.shows the relationship between the answers from the DR and the FFQ.All of the answer options are correct.
d
A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students' total times for one day are given below (in minutes). 45 57 63 79 84 92 99 105 117 145 A student who was not included in the survey recorded a time of 240 minutes on social media. That value is: clearly an erroneous recording. consistent with these data. inconsistent with these data. an outlier.
d
A survey of 10 students was conducted to investigate the amount of time they spend on social media each day. Students were given a timer and asked to record the number of minutes spent every time they accessed social media. The students' total times for one day are given below (in minutes). 45 576379849299105117145 The first quartile for these data is: 92 . 88 . 105 . 63 .
d
An appropriate graphical way to display housing (stall, small paddock, large paddock, pasture, or other housing) for horses is given by: a stemplot. a histogram. All of the answer options are correct. a pie chart.
d
Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths. The researchers decided to draw two histograms: one for horses with enteroliths (cases) and one for horses without (controls). The number of horses 20 years and older: is about the same for both. is larger among the cases. cannot be determined from the histogram. is smaller among the cases.
d
The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution? 88.3 % 15.7 % 100 % 11.7 %
d
The following is a scatterplot for profits versus sales (in tens of thousands of dollars) for a sample of 14 large companies. The correlation between sales and profits is 0.949 . From this information we see that: there is a clear error because profits cannot be negative. All of the answer options are correct. profits can be accurately predicted from sales. there is one very influential observation in the data.
d
What can be said of the correlation between the brand of an automobile and its quality? The correlation is negative, because smaller cars tend to have higher quality and larger cars tend to have lower quality. The correlation is positive, because better brands have higher quality. the correlation is negative, an arithmetic mistake was made; correlation must be positive. Correlation makes no sense here, because brand is a categorical variable.
d
Which of the following statements is false? Older children tend to be taller than younger children, so the correlation between age and height in children must be positive. Taller people tend to be heavier than shorter people, so the correlation between height and weight must be positive. Older men tend to have lower muscle density, so the correlation between age and muscle density in older men must be negative. A researcher finds that the correlation between two variables is close to 0 , so the two variables must be unrelated.
d
You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12 . Your score was 90 . Your friend had a time conflict and took a course with another instructor. Your friend had a score of 75 on a test, with a mean of 60 and a standard deviation of 10 . What can you conclude? The tests cannot be compared. You clearly ranked better. Your friend actually ranked better. You and your friend ranked equally well.
d
A Normal distribution: All of the answer options are correct. is symmetric. can be completely specified by a mean, 𝜇 , and a standard deviation, 𝜎 . has an area of exactly 1 underneath the density curve.
a
A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be: amount of eroded soil =0.4+1.3𝑥 (where 𝑥is flow rate). The correlation between amount of eroded soil and flow rate would be: positive, but we cannot say what the exact value is. 1/1.3 . 1.3 . either positive or negative, but it is impossible to say anything about the correlation from the information given.
a
Does exposure to classical music (through instrument lessons or concert attendance) improve a child's scholastic performance? In a study, researchers measured the amount of exposure to classical music for a group of children, along with their scores on the state's academic proficiency exam. The explanatory variable in this study is:the amount of exposure a child has to classical music. the child's score on the state's proficiency exam.the type of instrument a child plays.whether a child passed the state's proficiency exam.
a
The exam scores (out of 100 points) for all students taking an introductory statistics course are used to construct the following boxplot: If each person increased his or her score by 5 points, then: All of the answer options are correct. the third quartile would increase by 5 points. the interquartile range would remain unchanged. the median score would increase by 5 points.
a
The following is a sample of the percent increase in five growth funds over a one-year period. 8.9%12.2%13.7%14.4%9.8% The mean percent increase in this sample is: 11.8 %. 12.2 %. 13.7 %. 14.1 %.
a
The scores on the Wechsler Adult Intelligence Scale are approximately Normal, with 𝜇=100 and 𝜎=15 . The score needed to be among the highest 10 % of all scores is closest to: 119 . 75 . 81 . 125 .
a
The stemplot below displays midterm exam scores for 34 students taking a calculus course. The highest possible test score was 100 . The teacher declared that an exam grade of 65 or higher was good enough for a grade of C or better. 3 | 6 8 4 | 1 4 8 5 | 3 3 4 4 6 | 2 3 3 5 5 6 7 7 | 0 0 1 2 3 5 6 6 8 8 9 8 | 1 1 3 5 9 | 0 3 9 This stemplot is most similar to: a) a histogram with class intervals 30≤ score <40 , 40≤ score <50 , etc. b) a time plot of the data with the observations taken in increasing order. c) reporting the five-number summary for the data, with the mean. d) a boxplot of the data.
a
Your friend took an introductory statistics class last year and learned all about density curves. He draws a smooth curve with a long left tail. For such a curve, which of the following is true for the mean and median? mean < median mean > median There is not enough information to determine any of the answer options. mean = median
a
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The gender of each shopper was also obtained. The relationship between grocery expenditure and income was assessed by calculating both a correlation for the females only and a correlation for the males only. For the females, 𝑟=0.45 and for the males, 𝑟=0.38 . We conclude that: the relationship between grocery expenditures and income is stronger for males. the relationship between grocery expenditures and income is stronger for females. there is not enough information to determine which gender has a stronger relationship between grocery expenditures and income. the relationship between grocery expenditures and income is the same for males and females.
b
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The correlation was found to be 𝑟=0.649 . The amount of variation in the response explained by the regression line is: 0.649 %. 42.1 %. 0.421 %. 64.9 %.
b
Colleges often rely heavily on raising money for an "annual fund" to support operations. Alumni are typically solicited for donations to the annual fund. Studies suggest that the graduate's annual income is a good predictor of the amount of money he or she would be willing to donate, and there is a reasonably strong, positive, linear relationship between these variables. In the studies described:the correlation between annual income and the size of the donation is positive.All of the answer options are correct.annual income is an explanatory variable.the size of the donation to the annual fund is the response variable.
b
Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows: 10 20 4 13 21 16 16 The mean age for this group of stallions is: 16 . 14.3 . 12.5 . 13 .
b
Enteroliths are calcifications that form in the gut of horses. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as age, diet, and environment) that may be related to the formation of enteroliths. The histogram of age for the horses in the enteroliths study is: bimodal. slightly right-skewed. symmetric. slightly left-skewed.
b
The average salary of all female workers at a large plant is $35,000 . The average salary of all male workers at the plant is $41,000 . If there are more female workers than male workers at the plant, then the average salary at the plant must be: exactly $38,000 . smaller than $38,000 . larger than $38,000 . larger than $41,000 .
b
The data and the graph below show the scores students in an advanced statistics course received for homework (Hw) completed and for the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500 and the maximum midterm score was 350 . Hw score387275280459395314428366421234Exam score190200108323315256341236285125 The slope for the regression line is: −0.84 . 0.91 . 0.84 . 0.70 .
b
The proportion of the variation in the values of a response 𝑦 that is explained by the least-squares regression of 𝑦 on 𝑥 is: the slope of the least-squares regression line. the square of the correlation coefficient. the intercept of the least-squares regression line. the correlation coefficient.
b
The typical college freshman spends an average of 𝜇=150 minutes per day, with a standard deviation of 𝜎=50minutes, on social media. The distribution of time on social media is known to be Normal. The third quartile is: 0.75 minutes. 183.72 minutes. 116. 27 minutes. 0.25 minutes.
b
Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to -0.5<𝑍<1.2 is: 0.3085 . 0.5764 . 0.8849 . 0.2815 .
b
A frequent flyer was interested in the relationship between dollars spent on flying and the distance flown. She sampled 20frequent flyers of a certain airline. She collected the number of miles flown in the previous year and the total amount of money the flyer spent. A regression line of distance flown on money spent was fit to the data, and the intercept and slope were calculated to be 𝑎=24,000 and 𝑏=10 . One of the randomly sampled frequent flyer was found to have spent $2500 and flown 41000miles. The residual for this observation is: -16000 miles. 4000 miles. -8000 miles. 12000 miles.
c
A researcher obtained students' average SAT scores in each of the 50 states and the average teacher salaries in each of the 50states. She found a negative correlation between these variables. The researcher concluded that a lurking variable must be present. By "lurking variable," the researcher means: the true variable, which is explained by the explanatory variable. the true cause of a response. a variable that is not among the variables studied but that affects the response variable. any variable that produces a large residual.
c
A sample of 40 employees from the local Honda plant was obtained, and the length of time (in months) that each employee has worked at the plant was recorded. A stemplot of these data follows. In the stemplot, 5|2 represents 52 months. 5 | 2 2 3 3 4 5 7 8 9 9 6 | 0 0 0 2 3 4 4 4 5 6 7 7 8 8 8 9 7 | 3 4 5 5 6 6 7 7 7 8 8 9 9 8 | 9 | 8 What would be a better way to represent this data set? a) Display the data in a time plot. b) Use a histogram with class width equal to 10 . c) Split the stems. (not right) d) Use a pie chart.
c
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers to spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The explanatory variable is:gender.All of the answer options are correct.weekly income.weekly expenditure.
c
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The data below are for 10 selected survey participants: IncomeGrocery9852201782981083981214818060099738162805818901051023173 The scatterplot with a linear trend line is given below: If the expenditure for subject 7 is decreased and for subject 8 is increased, the effect on the correlation: will be no effect. will be to decrease it. cannot be determined without knowing the new values for expenditure. will be to increase it.
c
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The gender of the shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. IncomeGrocery9852201782981083981214818060099738162805818901051023173 The intercept of the regression line for these data is given by: 0.079 . 105.9 . 61.91 . 43.82 .
c
Consumers' Union measured the gas mileage per gallon of thirty-eight 1998-99 model automobiles on a special test track. The following pie chart provides information about the country of manufacture of the cars that Consumers' Union used. Based on this pie chart, we may conclude that: Swedish cars get gas mileages that are between those of Japanese cars and U.S. cars. Mercedes Benz, Audi, Porsche, and BMW represent approximately one-quarter of the cars tested. More than half of the cars in the study were from the United States. Japanese cars get significantly lower gas mileage than cars of other countries. We know this because their slice of the pie is at the bottom of the chart.
c
Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained 62 horses with enteroliths (cases) and 75 horses without (controls). The graph below contains side-by-side boxplots of the percent of alfalfa in the diet for cases and controls. Based on the boxplot cases, the median amount of alfalfa in the diet of cases is: None of the answer options is correct. half the amount as for controls. twice the amount as for controls. the same as for controls.
c
For this density curve, what percent of the observations lie above 0.2 ? 10 % 20 % 90 % 80 %
c
Some of the variables from a survey conducted by the U.S. Census Bureau are the number of people living in a household, the total household gross income, and the ages of household residents. Which of the variables is quantitative? the number of people living in a household the ages of household residents All of the answer options are correct. the total household gross income
c
The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 2004. In each class interval, the left endpoint but not the right is included, so the class intervals are 10≤ rate <15, 15≤ rate <20, etc. The number of schools with an acceptance rate over 30% is 12 . 5 . 13 . 10 .
c
