Statistics Final Exam
Which of the following is TRUE of the slope of the least-squares regression line?
It has the same sign as the correlation.
The table below presents the data for the on-time high school graduation rates in each of the 50 states and the District of Columbia. Because the stemplot preserves the actual value of the observations, it is easy to find the midpoint and the spread. What are they? Midpoint is__? The spread is___ to___? The distribution is? A. Roughly symmetric B. Right-skewed C. Left-skewed
Midpoint= 80 Spread= 50 to 88 C. Left skewed
Certain private water utilities in South Carolina charge a variable rate for the drinking water they provide to residences. One customer's bills over a 23-month period were used to fit a linear regression in an attempt to predict charges on future bills according to gallons consumed. The resulting regression equation is Bill Amount = 23.2 + (7.67 x Thousand Gallons)
On average, the bill amount increases by 7.67 dollars for each additional thousand gallons consumed.
According to the U.S. Census Bureau's Current Population Survey, the mean and median 2012 income of people at least 25 years old who had a bachelor's degree but no higher degree were $50,281 and $62,597. Which of these numbers is the mean and which is the median? Explain your reasoning.
The mean is $62,597 and the median is $50,281. This is because economic variables are usually skewed to the right, which pulls the mean above the median.
A double-blind, randomized comparative experiment compared the effect of the drug lorcaserin and a placebo on weight loss in overweight adults. All subjects also underwent diet and exercise counseling. The study reported that after one year, patients in the lorcaserin group had an average weight loss of 5.8 kilograms (kg), while those on the placebo had an average weight loss of 2.2 kg (P < 0.001). Select the most suitable sentence that describes the situation.
These results mean that there is good reason to think that lorcaserin works.
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree days, where a day's degree-days are the number of degrees its average temperature falls below 65 degrees F) over a 23-month period. By looking at the equation of the least-squares regression line (ŷ = 85 + 16x), you can see that the correlation between amount of gas used and degree-days is
greater than zero.
A woman is told her weight has a standard score (z-score) of -1.5. This means that
her weight is 1.5 standard deviations below average
A researcher wants to study the effects of regular exercise on cholesterol levels. The researcher compares the cholesterol levels of 50 people who belong to a local gym and exercise regularly with the cholesterol levels of 50 people from the community who do not exercise regularly. The cholesterol levels of the members of the gym were substantially lower. The researcher can conclude that
members of a local gym who exercise regularly have lower cholesterol levels than those in the community who do not exercise regularly.
You use software to carry out a test of significance. The program tells you that the P-value is P = 0.008. This result is
statistically significant at both α = 0.05 and α = 0.01.
The gas mileage for a particular model car is known to have a standard deviation of miles per gallon in repeated tests in a controlled laboratory environment at a fixed speed. For a fixed speed, gas mileages in repeated tests are Normally distributed. Tests on three cars of this model at 35 miles per hour give gas mileages of 24.3, 24.9, and 24.8 miles per gallon. The statistic for testing H0: μ = 25 miles per gallon based on these three measurements is
z = -0.577.
The Sanchez household is about to install solar panels to reduce the cost of heating their house. In order to know how much the solar panels help, they record their consumption of natural gas before the panels are installed. Gas consumption is higher in cold weather, so the relationship between outside temperature and gas consumption is important. Here are data for 12 consecutive months: Degree days 19 3 3 0 0 0 8 11 27 46 38 34 Gas used 32 2 1.6 1 0.7 0.7 1.6 3.1 5.1 7.7 7 6.1 Use your calculator or software: the correlation between degree days and overall gas used is about?
0.35
Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 years vary approximately normally with a mean of 185 milligrams per deciliter (mg/dl) and a standard deviation of 39 mg/dl. Approximately what percent of young women in this age group will have cholesterol levels of less than 150 mg/dl?
18.5%
What percent of the observations in a distribution are greater than the third quartile? 25% 50% 75%
25%
Florida played a key role in recent presidential elections. Voter registration records in February 2014 show that 39% of Florida voters are registered as Democrats and 35% as Republicans. (Most of the others did not choose a party.) To test a random digit dialing device that you plan to use to poll voters for the 2014 Senate elections, you use it to call 250 randomly chosen residential telephones in Florida. Of the registered voters contacted, 34% are registered Democrats.
39% and 35% are parameters and 34% is a statistic.
The lifetime of a 2-volt nonrechargeable battery in constant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime of less than
541.60 hours.
The distribution of the number of graduate students over the past 13 years in the math department was: What is the smallest and largest number of students over the past 13 years? A. 16 and 49 B. 16 and 90 C. 16 and 73 D. 19 and 73
C. 16 and 73
Figure 1.6, below, is a histogram of the percent of on-time high school graduates in each state. The leftmost bar in the histogram covers percents of on-time high school graduates ranging from about? A. 0% to 58%. B. 58% to 61%. C. 58% to 64%.
C. 58% to 61%
The points on a scatterplot lie close to the line whose equation is y = 4 − 3x . The slope of this line is
-3
The lifetime of a 2-volt nonrechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. The proportion of batteries with lifetimes exceeding 520 hours is approximately
0.4207.
For a biology project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.76. If you had measured tail length in centimeters instead of millimeters, what would be the correlation?
0.76
The response variable in a study in which college students drank different amounts of beer, was their blood alcohol content (BAC). BAC for the same amount of beer might depend on other facts about the students. Select two other variables that would most likely influence BAC. Time spent consuming the beer. Student height. Student weight. Student age.
1,3
Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are five years' data on prices paid to coffee growers in Indonesia Price ($US per pound) 0.34 0.44 0.62 0.47 0.62 Forest lost (percent) 0.77 1.88 1.47 1.53 3.04 What is the correlation (± 0.01) between the price of coffee and the forest loss in US dollars? What is the correlation (± 0.01) between the price of coffee and the forest loss in Russian rubles, if the exchange rate is 26 Russian rubles per US dollar ?
1. 0.69 2. 0.69
The most common intelligence quotient (IQ) scale is normally distributed with a mean of 100 and a standard deviation of 15. Many school districts across the country seek to identify "gifted and talented" children for special enrichment programs. Typically, these children must have IQ scores in the top 5%. What is the minimum score to qualify a child for these programs?
125
A class survey in a large class for first-year college students asked, About how many hours do you study during a typical week? The mean response of the 463 students was x = 15.3 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 8.5 hours in the population of all first-year students at this university. Use the survey result to give a 99% confidence interval for the mean study time of all first-year students.
14.28 to 16.32
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree days, where a day's degree-days are the number of degrees its average temperature falls below 65 degrees F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be y= 18+16x How much, on average, does gas used increase for each additional degree-day?
16
An instructor in a large lecture class found at the end of the semester that the total point distribution in his class was approximately normal with a mean of 530 and a standard deviation of 80. If 10% of the class are to receive As (the instructor grades on a curve), what is the lowest number of points for a student to earn an A?
632
(5.20) Figure 5.10 (below) is a scatterplot of school GPA against IQ test scores for 15 seventh-grade students. The line is the least-squares regression line for predicting school GPA from IQ score. If another child in this class has IQ score 110, you predict the school GPA to be close to
7.5
An instructor in a large lecture class found at the end of the semester that the total point distribution in his class was approximately normal with a mean of 530 and a standard deviation of 80. About what percent of students will score between 370 and 690?
95%
Where do students go to school? Although 81.4% of first time first-year students attended college in the state in which they lived, this percent varied considerably over the states. Here is a stemplot of the percent of first-year students in each of the 50 states who were from the state where they enrolled. The stems are 10s and the leaves are 1s. The stems have been split in the plot. The midpoint of this distribution is? A. 80%. B. 83%. C. 65%
A. 80%
Figure below is a histogram of the percent of on-time high school graduates in each state. The highest bar in the histogram covers percents of on-time high school graduates ranging from about? A. 82% to 85% B. 82% to 88% C. 0% to 82%
A. 82% to 85%
When ordering vinyl replacement windows, the following variables are specified for each window. Which of these variables is quantitative? A.area of the window opening in square inches B.window style — double-hung, casement, or awning C.window style — single pane or double-hung
A. Area of the window opening in square inches
A statistics professor asked her students on the first day of class to report their grade point averages (GPAs) as part of a class survey. For those students who knew their GPA, the histogram was A. left-skewed. B. right-skewed. C. symmetric.
A. Left Skewed
The histogram below shows the distribution of the annual hours of commuting delay per traveler for 46 small and medium urban areas (fewer than 1 million in population). Which measure of center and variability would be most appropriate to report for this distribution? A. median and quartiles B. mean and standard deviation C. mean and quartiles D. median and standard deviation
A. Median and quartiles
States differ greatly in the percentage of residents born outside the United States. California leads with 26.5% foreign-born. The figure below is a histogram of the distribution of foreign-born residents (by percentage) in the United States. What is the shape of this distribution? A. Skewed right B. Symmetrical C. Skewed left
A. Skewed right
A description of different houses on the market includes the variables square footage of the house and the average monthly gas bill A. Square footage and average monthly gas bill are both quantitative variables. B. Square footage and average monthly gas bill are both categorical variables. C. Square footage is a categorical variable and average monthly gas bill is a quantitative variable.
A. Square footage and average monthly gas bill are both quantitative variables.
A teacher gave a 25 question multiple-choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this information? A. all the students had the same score. B. she must have made a mistake. C. about half the scores were above the mean.
A. all the students had the same score
If a distribution is skewed to the left, A. the mean is less than the median. B. the mean and median are equal. C. the mean is greater than the median.
A. the mean is less than the median
The National Institute of Standards and Technology (NIST) supplies a "standard iron rod" whose electrical conductivity is supposed to be exactly 10.1. Is there reason to think that the true conductivity is not 10.1? To find out, NIST measures the conductivity of one rod 6 times. Repeated measurements of the same thing vary, which is why NIST makes 6 measurements. These measurements are an SRS from the population of all possible measurements. This population has a Normal distribution with mean μ μ equal to the true conductivity and standard deviation σ σ = 0.1. We seek evidence against the claim that μ = 10.1. What is the sampling distribution of the mean x in many samples of 6 measurements if the claim is true?
Approximately Normal with mean 10.1 and standard deviation 0.041.
A survey of college students collected information on several variables: Distance from Home, Age, Major, Gender, and Class. The variable Class is A. quantitative. B. categorical. C. neither categorical nor numeric.
B. Categorical
A political party's data bank includes the zip codes of past donors, such as Zip code is a? A. quantitative variable. B. categorical variable. C. unit of measurement.
B. Categorical value
You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to $500,000 in price. The few houses on the water, however, have prices up to $15 million. The distribution of house prices will be? A. roughly symmetric. B. skewed to the right. C. skewed to the left.
B. Skewed to the right
Students who have finished medical school are assigned to residencies in hospitals to receive further training in a medical specialty. Here is part of a hypothetical database of students seeking residency positions. USMLE is the student's score on Step 1 of the national medical licensing examination. A. Residency positions. B. Students who have finished medical school. C. Medical schools. D. Student's scores.
B. Students who have finished medical school
The bars on a histogram A.sometimes touch one another. B.never touch one another. C.always touch one another.
C. Always touch one another
Consumer Reports is doing an article comparing refrigerators in their next issue. Some of the characteristics to be included in the report are the brand name and model; whether it has a top, bottom, or side-by-side freezer; the estimated energy consumption per year (kilowatts); whether or not it is Energy Star compliant; the width, depth, and height in inches; and both the freezer and refrigerator net capacity in cubic feet. The "Energy Star compliant" is categorical variable, quantitative variable, or individuals? A. individuals B. quantitative variable C. categorical variable
C. Categorical Variable
A high level of glucose in the blood is an indication of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications, such as blindness and heart disease. A random sample of 180 individuals had their blood sugar level measured. The results are displayed in the graph. A. skewed to the left. B. symmetric. C. skewed to the right.
C. Skewed to the right
Here are the first lines of a professor's data set at the end of a statistics course: The individuals in these data are A. the total points. B. the course grades. C. the students.
C. The students
A high level of glucose in the blood is an indication of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications, such as blindness and heart disease. A random sample of 180 individuals had their blood sugar level measured. The results are displayed in the graph. Which value might be considered an outlier in the distribution of blood glucose? A. 39 B. 145 C. 175 D. 215
D. 215
Figure 1.15 (below) is a stemplot of the IQ test scores of 78 seventh-grade students in a rural midwestern school. Four students had low scores that might be considered outliers. Ignoring these, describe the shape, center, and spread of the distribution. (Notice that it looks roughly bell-shaped.) A. Fairly symmetric, with center near 104. Ignoring the outliers, the range is from 8 to 13. B. Slightly right-skewed with center near 104 and range from 72 to 136. C.Slightly left-skewed with center near 110. Ignoring the outliers, the range is from 86 to 136. D. Fairly symmetric with center near 110 and range from 86 to 136. We often read that IQ scores for large populations are centered at 100. What percent of these 78 students have scores above 100? Round your answer to one decimal place. Fill in the blank:
D. Fairly symmetric with center near 110 and range from 86 to 136. 79.5 82.1
Consumer Reports often reviews current-model-year cars. The boxplots below can help us compare the 0 to 60 mph acceleration times (in seconds) of cars in several categories: small cars (4-cylinder engines), family sedans, large sedans, upscale sedans (all 6-cylinder engines), and luxury sedans (a mixture of 6- and 8-cylinder engines). The smaller the acceleration time, the faster the car accelerates. In which category was the car with the fastest acceleration (that is, the shortest acceleration time)? A. large B. luxury C. small D. upscale
D. upscale
Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus. The sample mean is x = 16.5 seconds. The null hypothesis for the significance test is
H0 : μ = 18.
Missy took the ACT and was told her standard score (z-score) is -1. Frank took the SAT and was told his standard score (z-score) is -2. Which student has a better chance of getting admitted to college based on their test score?
Missy
An archaeological dig turns up large numbers of pottery shards, broken stone implements, and other artifacts. Students working on the project classify each artifact and assign it a number. The counts in different categories are important for understanding the site, so the project director chooses 2% of the artifacts at random and checks the students' work. What are the population and the sample here?
Population: All artifacts discovered in the dig. Sample: The selected 2% of the artifacts.
An online store contacts 1000 customers from its list of customers who have purchased something from them in the last year. In all, 696 of the 1000 say that they are very satisfied with the store's Web site. The population in this setting is
all customers who have purchased something in the last year.
There seems to be a clear relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a midwestern city over a period of 18 months. A scatterplot of the data collected shows that the linear model is appropriate. The equation of the least-squares regression line is Number of new houses = 672.89 - (30.65 × interest rate) and r2 = 0.49 The association or direction between the interest rate and the number of new houses being built is
negative
The National Assessment of Educational Progress (NAEP) includes a mathematics test for eigth-grade students. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 900 8th-graders from a large population in which the scores have mean = 285 and standard deviation σ = 125. The mean will vary if you take repeated samples. Suppose that we took an SRS of 1600 8th-graders and found =288. Compared with an SRS of 900 8th-graders, the margin of error for a 95% confidence interval for is
smaller.
A state representative wants to know how voters in his district feel about enacting a statewide smoking ban in all enclosed public places, including bars and restaurants, as well as several other current statewide issues. He mails a questionnaire addressing these issues to an SRS of 800 voters in his district. Of the 800 questionnaires mailed, 152 were returned. The sample is
the 152 voters returning the questionnaire.
