AP STATS MIDTERM
An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that a. when corn prices are above average, soybean prices also tend to be above average. b. there is almost no relation between corn prices and soybean prices. c. when corn prices are above average, soybean prices tend to be below average. d. when soybean prices go up by 1 dollar, corn prices go up by 70 cents. e. the economist is confused, because correlation makes no sense in this situation.
a
Control groups are used in experiments in order to: a. control the effects of outside variables on the outcome. b. control the subjects of a study to ensure that all participate equally. c. guarantee that someone other than the investigators, who have a vested interest in the outcome, controls how the experiment is conducted. d. achieve a proper and uniform level of randomization. e. reduce the variability in results.
a
For the density curve shown below, which statement is true? a. The area under the curve between 0 and 1 is 1. b. The density curve is symmetric. c. The density curve is skewed right. d. The density curve is Normal. e. None of the above is correct.
a
Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study, a. gas mileage is a response variable, and you expect to find a negative association. b. gas mileage is a response variable, and you expect to find a positive association. c. gas mileage is an explanatory variable, and you expect to find a strong negative association. d. gas mileage is an explanatory variable, and you expect to find a strong positive association. e. gas mileage is an explanatory variable, and you expect to find very little association.
a
Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern? a. A straight line is not a good model for the data. b. The correlation must be 0. c. The correlation must be positive. d. Outliers must be present. e. The regression line might or might not be a good model for the data, depending on the extent of the curve.
a
The mean speed of vehicles in the "cars only" lanes of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lanes is 64 miles per hour. What must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes? a. It could be any number between 64 and 68 miles per hour. b. It must be larger than the median speed. c. It must be larger than 66 miles per hour. d. It must be 66 miles per hours. e. We don't have enough information to draw any conclusion about the mean speed of all vehicles.
a
The proportion of scores in a standard Normal distribution that are greater than 1.25 is closest to: a. .1056 b. .1151 c. .1600 d. .8849 e. .8944
a
Which of the following statements are true? I. The area under a Normal curve is always 1, regardless of the mean and standard deviation. II. The mean is always equal to the median for any Normal distribution. III. The interquartile range for any Normal curve extends from a. I and II b. I and III c. II and III d. I, II, and III e. None of the above gives the correct set of true statements.
a
Which of these variables is least likely to have a Normal distribution? a. Annual income for all 150 employees at a local high school b. Lengths of 50 newly hatched pythons c. Heights of 100 white pine trees in a forest d. Amount of soda in 60 cups filled by an automated machine at a fast-food restaurant e. Weights of 200 of the same candy bar in a shipment to a local supermarket
a
A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations give = 8.4, = 2.1, = 14.2, = 3.8, and r = 0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers? a. 0.86 b. 1.56 c. 0.48 d. 2.82 e. Can't tell from the information given
b
A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is = 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements is not necessarily true? a. For each one-point increase in performance rating, the raise will increase on average by $2000. b. The actual relationship between salary raises and performance rating is linear. c. A rating of 0 will yield a predicted raise of $1400. d. The correlation between salary raise and performance rating is positive. e. If the average performance rating is 1.2, then the average raise is $3800.
b
A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following describes how the company's mean and median salaries would change? a. The mean and median would both increase by $5,000. b. The mean would increase by $5,000 and the median would not change. c. The mean would increase by $6,000 and the median would not change. d. The median would increase by $6,000 and the mean would not change. e. The mean would increase by $6,000, but we cannot determine the change in the median without more information.
b
For the distribution of cookie bags described in Question 3, approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)? a. 10 b. 16 c. 32 d. 64 e. None of the above
b
Here are the IQ test scores of 10 randomly chosen fifth-grade students: To make a stemplot of these scores, you would use as stems a. 0 and 1. b. 09, 10, 11, 12, 13, and 14. c. 96, 110, 118, 122, 125, 126, 130, 139, and 145. d. 0, 2, 3, 5, 6, 8, 9. e. None of the above is a correct answer.
b
In the course described in #2, Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual? a. -2.0 b. 2.0 c. 3.0 d. 93 e. None of these
b
Kitchen appliances don't last forever. The lifespan of all microwave ovens sold in the United States is approximately Normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage of the ovens last more than 10 years? a. 11.5% b. 34.5% c. 65.5% d. 69% e. 84.5%
b
Loretta is 20 months old and is 80 centimeters tall. What is her residual? a. 2.47 b. 2.47 c. -12.60 d. 12.60 e. 77.53
b
Mr. Yates picked up a dozen items in the grocery store with a mean cost of $3.25. Then he added an apple pie for $6.50. The new mean for all 13 items is a. $3.00 b. $3.50 c. $3.75 d. $4.88 e. None of the above
b
On May 11, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice—the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be: a. near zero, as morning and afternoon readings should be independent. b. high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon. c. high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon. d. near zero, as correlation measures the strength of the linear association. e. near zero, as blood pressure readings should follow approximately a Normal distribution.
b
One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that a. minimizes the sum of the distances between the actual UV values and the predicted UV values. b. minimizes the sum of the squared residuals between the actual yield and the predicted yield. c. minimizes the sum of the distances between the actual yield and the predicted UV. d. minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values. e. minimizes the perpendicular distance between the regression line and each data point.
b
The density curve below takes the value 0.5 on the interval 0 = x = 2 and takes the value 0 everywhere else. What percent of the observations lie between 0.5 and 1.2? a. 25% b. 35% c. 50% d. 68% e. 70%
b
The distribution of the heights of students in a large class is roughly Normal. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Thus, the standard deviation of the height distribution is approximately equal to: a. 2 b. 3 c. 6 d. 9 e. 12
b
The heights of American men aged 18 to 24 are approximately Normally distributed with a mean of 68 inches and a standard deviation of 2.5 inches. Only about 5% of young men have heights outside the range a. 65.5 inches to 70.5 inches b. 63 inches to 73 inches c. 60.5 inches to 75.5 inches d. 58 inches to 78 inches e. none of the above
b
The pie chart at right describes the distribution of favorite school subject for 300 high school students. Which of the following can we conclude from this graph? a. Math was the favorite subject for 26 students. b. English was the favorite subject of 96 students. c. Taken together, history, English, and the arts where the favorite subjects of less than half the students. d. No student said that Spanish was his or her favorite subject. e. Most of the English students were female.
b
To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is a. an observational study. b. a matched pairs experiment. c. a completely randomized experiment. d. a block design, but not a matched pairs experiment. e. impossible to classify unless more details of the study are provided.
b
We wish to draw a sample of 5 without replacement from a population of 50 households. Suppose the households are numbered 01, 02, . . . , 50, and suppose that the relevant line of the random number table is Then the households selected are a. households 11 13 36 62 73 b. households 11 36 23 08 42 c. households 11 36 23 23 08 d. households 11 36 23 56 92 e. households 11 35 96 90 46
b
You have data for many families on the parents' income and the years of education their eldest child completes. Your initial examination of the data indicates that children from wealthier families tend to go to school for longer. When you make a scatterplot, a. the explanatory variable is parents' income, and you expect to see a negative association. b. the explanatory variable is parents' income, and you expect to see a positive association. c. the explanatory variable is parents' income, and you expect to see very little association. d. the explanatory variable is years of education, and you expect to see a negative association. e. the explanatory variable is years of education, and you expect to see a positive association.
b
A fire department in a rural county reports that its response time to fires is approximately Normally distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what proportion of their response times is over 30 minutes? a. 0.03 b. 0.21 c. 0.25 d. 0.75 e. 0.79
c
A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model? a. A residual plot is not an appropriate means for evaluating a linear model. b. The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players. c. The curved pattern in the residual plot suggests that the linear model is not appropriate. d. There are not enough data points to draw any conclusions from the residual plot. e. The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.
c
A medical researcher collects health data on many women in each of several countries. One of the variables measured for each woman in the study is her weight in pounds. The following list gives the five-number summary for the weights of adult women in one of the countries. About what percent of Country A women weigh between 110 and 240 pounds? a. 50% b. 65% c. 75% d. 85% e. 95%
c
A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information you conclude a. that the remedy is effective for the treatment of headaches. b. nothing, because the sample size is too small. c. nothing, because there is no control group for comparison. d. that the new treatment is better than aspirin. e. that the remedy is not effective for the treatment of headaches.
c
A researcher for a consumer products company is field testing a new formula for laundry detergent. He has contracted with 60 families, each with two children, who have agreed to test the product. He randomly assigns 30 families to the group that will use the new formula and 30 to the group that will use the company's current detergent formula. The most important reason for this random assignment is that a. randomization makes the analysis easier since the data can be collected and entered into the computer in any order. b. randomization eliminates the impact of any confounding variables. c. randomization is a good way to create two groups of 30 families that are as similar as possible, so that comparisons can be made between the two groups. d. randomization ensures that the study is double-blind. e. randomization reduces the impact of outliers.
c
A researcher observes that, on average, the number of divorces in cities with Major League Baseball teams is larger than in cities without Major League Baseball teams. The most plausible explanation for this observed association is that the a. presence of a Major League Baseball team causes the number of divorces to rise (perhaps husbands are spending too much time at the ballpark). b. high number of divorces is responsible for the presence of Major League Baseball teams (more single men means potentially more fans at the ballpark, making it attractive for an owner to relocate to such cities). c. association is due to the presence of a lurking variable (Major League teams tend to be in large cities with more people, hence a greater number of divorces). d. association makes no sense, since many married couples go to the ballpark together. e. observed association is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.
c
A researcher reports that the participants in his study lost a mean of 10.4 pounds after two months on his new diet. A friend of yours comments that she tried the diet for two months and lost no weight, so clearly the report was a fraud. Which of the following statements is correct? a. Your friend must not have followed the diet correctly, since she did not lose weight. b. Since your friend did not lose weight, the report must not be correct. c. The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even that all lost weight. Your friend's experience does not necessarily contradict the study results. d. In order for the study to be correct, we must now add your friend's results to those of the study and recompute the new average. e. Your friend is an outlier.
c
A sample of 250 high school students were asked, "If you had $1000 to contribute to one kind of charitable organization, which type of organization would you choose? Below is a two-way table of responses to this question and gender.Which of the following conclusions seems to be supported by the data? a. Most of the females who chose a health organization would have chosen an environmental organization as their second choice, had they been asked. b. There is no association between gender and choice of organization. c. The proportion of males who said they would contribute to an environmental organization was higher than the proportion of females who said they would contribute such an organization. d. None of the students surveyed said they would contribute to religious organizations. e. The marginal distribution of Organization is 140, 110.
c
A sample of 99 distances has a mean of 24 feet and a median of 24.5 feet. Unfortunately, it has just been discovered that the maximum value in the distribution, which was erroneously recorded as 40, actually had a value of 50. If we make this correction to the data, then a. the mean remains the same, but the median is increased. b. the mean and median remain the same. c. the median remains the same, but the mean is increased. d. the mean and median are both increased. e. we do not know how the mean and median are affected without further calculations, but the variance is increased.
c
Below is a cumulative relative frequency graph for the 48 racers who finished the grueling 50km cross-country ski race at the 2010 Vancouver Olympics. Approximately what proportion of the racers finished the race in more than 2.15 hours? a. 0.17 b. 0.40 c. 0.45 d. 0.50 e. 0.55
c
For the density curve shown in Question 33, which statement is true? a. The mean and median are equal. b. The mean is greater than the median. c. The mean is less than the median. d. The mean could be either greater than or less than the median. e. None of the above is correct.
c
For the density curve shown in Question 41, which statement is true? a. The mean is greater than the median. b. The mean is less than the median. c. The mean and median are equal. d. The mean could be either greater than or less than the median. e. None of the above is correct.
c
If your score on a test is at the 60th percentile, you know that your score lies a. below the first quartile. b. between the first quartile and the median. c. between the median and the third quartile. d. above the third quartile. e. There is not enough information to say where it lies relative to the quartiles.
c
In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines? a. 86% b. 93% c. 74% d. 55% e. Can't tell from the information given
c
Leonardo da Vinci, the renowned painter, speculated that an ideal human would have an armspan (distance from the outstretched fingertip of the left hand to the outstretched fingertip of the right hand) that was equal to his height. The following computer regression printout shows the results of a least-squares regression of armspan on height, both in inches, for a sample of 18 high school students. Which of the following statements is false? a. This least-squares regression model would make a prediction that is 1.64 inches higher than da Vinci projected for a 62-inch tall student. b. If one of the students in the sample had a height of 70.5 inches and an armspan of 68 inches, then the residual for this student would be -2.78 inches. c. The least-squares regression line has a steeper slope than the equation for da Vinci's relationship between armspan and height. d. For every one-inch increase in height, the regression model predicts about a 0.84-inch increase in armspan. e. For a student 66 inches tall, our model would predict an armspan of about 67 inches.
c
Mr. Nerdly asked the students in his AP Statistics class to report their overall grade point averages and their SAT Math scores. The scatterplot below provides information about his students' data. The dark line is the least-squares regression line for the data, and its equation is . Which of the following statements about the circled point is false? a. This student has a grade point average of about 2.9 and an SAT Math score of about 690. b. If we used the least-squares line to predict this student's SAT Math score, we would make a prediction that is too low. c. This student's residual is negative. d. Removing this data point would cause the correlation coefficient to increase. e. Removing this student's data point would increase the slope of the least-squares line.
c
Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will contain between 16.0 and 16.1 ounces is about a. 10 b. 16 c. 34 d. 68 e. None of the above is correct.
c
The Interquartile range for the distribution of 50 states in the previous question is: a. 11.7% to 13.5% b. 117% to 135% c. 1.8% d. 2.7% e. 18%
c
The area under the standard Normal curve corresponding to -0.3 < Z < 1.6 is a. 0.3273 b. 0.4713 c. 0.5631 d. 0.9542 e. none of the above
c
The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be a. much smaller than 0.52 b. slightly smaller than 0.52 c. unchanged: equal to 0.52 d. slightly larger than 0.52 e. much larger than 0.52
c
The five-number summary for scores on a statistics exam is 11, 35, 61, 70, 79. In all, 380 students took the test. About how many had scores between 35 and 61? a. 26 b. 76 c. 95 d. 190 e. None of these
c
The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude that a. owners of other brands of trucks are less satisfied than the owners of these three brands. b. Chevrolet owners are substantially more satisfied than Ford or Toyota owners. c. there is very little difference in the satisfaction of owners for the three brands. d. Chevrolet probably sells more trucks than Ford or Toyota. e. a pie chart would have been a better choice for displaying these data.
c
The following is a histogram showing the actual frequency of the closing prices of a particular stock on the New York Stock Exchange over a 50-day period. The class that contains the third quartile is: a. 10-20 b. 20-30 c. 30-40 d. 40-50 e. 50-60
c
The graph below is a Normal probability plot for the amount of rainfall (in acre-feet) obtained from 26 randomly selected clouds that were seeded with silver oxide. Which of the following statements about the shape of the rainfall distribution is true? a. The distribution is Normal. b. The distribution is approximately Normal. c. The distribution is skewed left. d. The distribution has no potential outliers. e. The distribution is skewed right.
c
The mean age (at inauguration) of all U.S. Presidents is approximately Normally distributed with a mean of 54.6. Barack Obama was 47 when he was inaugurated, which is the 11th percentile of the distribution. Which of the following is closest to the standard deviation of presidents' ages? a. -9.20 b. -6.18 c. 6.18 d. 7.60 e. 9.20
c
The proportion of observations from a standard Normal distribution that take values larger than -0.75 is about a. 0.2266 b. 0.7704 c. 0.7734 d. 0.7764 e. 0.8023
c
There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by predicted height = 50.3 + 6.01(age) where height is measured in centimeters and age in years. Which of the following is not correct? a. The estimated slope is 6.01, which implies that female children between the ages off 5 and 18 increase in height by about 6 cm for each year they grow older. b. The estimated height of a female child who is 10 years old is about 110 cm. c. The estimated intercept is 50.3 cm. We can conclude from this that the typical height of female children at birth is 50.3 cm. d. The average height of female children when they are 5 years old is about 50% of the average height when they are 18 years old. e. My niece is about 8 years old and is about 115 cm tall. She is taller than average for girls her age.
c
Use the information in the previous problem (31). About what percentage of the men are over 70.5 inches tall? a. 2.5 b. 5 c. 16 d. 32 e. 68
c
When testing water for chemical impurities, results are often reported as bdl, that is, below detection limit. The following are the measurements of the amount of lead in a series of water samples taken from inner-city households (in parts per million) Which of the following statements can we be sure is true? a. The mean lead level in the water is about 10 ppm. b. The mean lead level in the water is about 9 ppm. c. The median lead level in the water is 7 ppm. d. The median lead level in the water is 8 ppm. e. Neither the mean nor the median can be computed because some values are unknown.
c
Which of the following is correct? a. If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg. b. If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units. c. If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg. d. The predicted yield is 4.3 kg when the UV value is 20 Dobson units. e. None of the above is correct.
c
Which of the following properties is true for all Normal density curves? I. They are symmetric. II. The curve reaches its peak at the mean. III. 95% percent of the area under the curve is within one standard deviation of the mean. a. I only b. II only c. I and II only d. I and III only e. All three statements are correct.
c
Which of the following statements is/are true? I. Correlation and regression require that there are clearly-identified explanatory and response variables. II. Scatterplots require that both variables be quantitative. III. Every least-squares regression line passes through a. I and II only b. I and III only c. II and III only d. I, II, and III e. None of the above
c
A maple sugar manufacturer wants to estimate the average trunk diameter of Sugar Maples trees in a large forest. There are too many trees to list them all and take a SRS, so he divides the forest into several hundred 10 meter by 10 meter plots, selects 25 plots at random, and measures the diameter of every Sugar Maple in each one. This is an example of a a. multistage sample. b. stratified sample. c. simple random sample. d. cluster sample. e. convenience sample.
d
A nutritionist wants to study the effect of storage time (6, 12, and 18 months) on the amount of vitamin C present in freeze dried fruit when stored for these lengths of time. Vitamin C is measured in milligrams per 100 milligrams of fruit. Six fruit packs were randomly assigned to each of the three storage times. The treatment, experimental unit, and response are respectively: a. A specific storage time, amount of vitamin C, a fruit pack b. A fruit pack, amount of vitamin C, a specific storage time c. Random assignment, a fruit pack, amount of vitamin C d. A specific storage time, a fruit pack, amount of vitamin C e. A specific storage time, the nutritionist, amount of vitamin C
d
A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation. Which of the following conclusions seems to be supported by the data? a. Republicans outnumber both Democrats and "Other." b. The conditional distribution of party affiliation for males is 1100. c. The marginal distribution of party affiliation is 1000, 1000. d. There is an obvious association between gender and political party registration. e. It is unclear whether there is an association between gender and political party registration.
d
A small company estimating its photocopying expenses finds that the mean number of copies made per day for the past 12 months is 258 copies per day with a standard deviation of 24 copies per day. Which of the following is a correct interpretation of standard deviation? a. The number of copies made per day was always between 234 and 282. b. About 95% of the time, the number of copies made per day was between 234 and 282. c. The difference between the mean number of copies made per day and the median number of copies made per day was 24. d. On average, the number of copies made each day was about 24 copies per day away from the mean, 258. e. 1.5 times the interquartile range of copies made per day is 24.
d
A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties X and O are represented by x's and o's, respectively, in the following scatterplot. Which of the following statements is true? a. Considering Variety X only, there is a positive correlation between sepal length and width. b. Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope. c. Considering both varieties together, there is a negative correlation between sepal length and width. d. Considering each variety separately, there is a negative correlation between sepal length and width. e. Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope.
d
A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least-squares line was fit to the data. Here is the residual plot from this least-squares fit. What does the residual plot tell you about the linear model? a. The residual plot confirms the linearity of the fuel economy data. b. The residual plot does not confirm nor rule out the linearity of the data. c. The residual plot suggests that the model may be linear, but more data points are needed to confirm this. d. The residual plot clearly indicates that the data isn't linear. e. A residual plot is not an appropriate means for evaluating a linear model.
d
A survey is to be administered to recent graduates of a certain nursing school in order to compare the starting salaries of women and men. For a random sample of graduates, three variables are to be recorded: sex, starting salary, and area of specialization. Which of the follow best describes a conclusion that can be drawn from this study? a. Whether being female causes graduates of this nursing school to have lower (or higher) starting salaries than males. b. Whether being female causes graduates in this sample to have lower (or higher) starting salaries than males. c. Whether choosing certain area of specialization causes females graduates of this nursing school to have lower (or higher) starting salaries than males. d. Whether there is an association between sex and starting salary among graduates of this nursing school. e. Whether there is an association between sex and starting salary at all nursing schools similar to this one.
d
According to the U.S. Bureau of Labor Statistics, the monthly percentage change in the number of jobs in a certain state for the twelve months of 2007 had a mean of 0.08% and a standard deviation of 1.70%. From this information we can conclude that a. The largest monthly change was 1.78% b. The distribution of monthly changes is strongly skewed to the right. c. Most of the monthly changes were negative. d. The magnitude of the monthly deviations from the mean change averaged about 1.70%. e. A mistake has been made. It makes no sense for the standard deviation to be greater than the mean.
d
Are jet skis (otherwise known as personal watercraft, or PWC) dangerous? An article in the August 1997 issue of the Journal of the American Medical Association reported on a survey that tracked emergency room visits at randomly selected hospitals nationwide. The study recorded data on the number of jet skis in use and the number of accidents related to their use for the years 1990-1995. Computer output and a residual plot from a linear regression of jet-ski related injuries versus jet skis in use (PWC) are shown below. Use Scenario 3-16. The circled point represents a year when the number of PWC in use was 240,000. The number of observed injuries in that year was closest to: a. 350 b. 1250 c. 1600 d. 2800 e. 7300
d
For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Joseph is 22.5 months old. What is his predicted height? a. 50.80 b. 64.96 c. 65.96 d. 79.11 e. 87.40
d
For the data in the previous problem (27), which measures of center and spread would be most appropriate to use? a. Mean and standard deviation b. Mean and interquartile range c. Mean and range d. Median and interquartile range e. Median and standard deviation
d
For the density curve shown, which statement is true? a. The density curve is Normal. b. The density curve is skewed right. c. The density curve is skewed left. d. The density curve is symmetric e. None of the above is correct.
d
If a store runs out of advertised material during a sale, customers become upset, and the store loses not only the sale but also goodwill. From past experience, a music store finds that the mean number of CDs sold in a sale is 845, the standard deviation is 15, and a histogram of the demand is approximately Normal. The manager is willing to accept a 2.5% chance that a CD will be sold out. About how many CDs should the manager order for an upcoming sale? a. 1295 b. 1070 c. 935 d. 875 e. 860
d
If data set A of (x, y) data has correlation r = 0.65, and a second data set B has correlation r = -0.65, then a. the points in A fall closer to a linear pattern than the points in B. b. the points in B fall closer to a linear pattern than the points in A. c. A and B are similar in the extent to which they display a linear pattern. d. you can't tell which data set displays a stronger linear pattern without seeing the scatterplots. e. a mistake has been made—r cannot be negative.
d
In a statistics course, a linear regression equation was computed to predict the final-exam score from the score on the first test. The equation was = 10 + 0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam? a. 85.5 b. 90 c. 95 d. 95.5 e. None of these
d
In some courses (but certainly not in an intro stats course!), students are graded on a "Normal curve." For example, students within ± 0.5 standard deviations of the mean receive a C; between 0.5 and 1.0 standard deviations above the mean receive a C+; between 1.0 and 1.5 standard deviations above the mean receive a B-; between 1.5 and 2.0 standard deviations above the mean receive a B, etc. The class average on an exam was 60 with a standard deviation of 10. The bounds for a B- grade and the percent of students who will receive a B- grade if the marks are actually Normally distributed are a. (65, 75), 24.17% b. (65, 75), 12.08% c. (70, 75), 18.38% d. (70, 75), 9.19% e. (70, 75), 6.68%
d
In the previous question, the mean finish time is 2.164 hours and the standard deviation is 0.85 hours. The distribution is skewed right. What are the mean, standard deviation, and shape of the distribution of z-scores of the same data? a. Mean = 2.164, Standard deviation = 0.85, skewed right b. Mean = 2.164, Standard deviation = 0.85, skewed left c. Mean = 2.164, Standard deviation = 0.85, approximately normal d. Mean = 0, Standard deviation = 1, skewed right e. Mean = 0, Standard deviation = 1, approximately normal
d
The bar graph shows the distribution of breeds for all the champions of the annual World Canine Disc Championships from 1975 to 2009. Which of the following statement can be made on the basis of this graph? a. Mixed breed dogs have won the championship about twice as often as Australian Shepherds. b. Most of the mixed breed dogs were at least half Border Collie. c. None of the champion dogs were Labrador Retrievers. d. The graph exaggerates the difference between the number of champions of each breed category. e. Border Collies are larger dogs than Australian Shepherds.
d
The cumulative relative frequency graph below shows the distribution of lengths (in centimeters) of fingerlings at a fish hatchery. The interquartile range for this distribution is approximately: a. 0.18 to 0.85 centimeters b. 5 to 7 centimeters c. 5.5 to 6.7 centimeters d. 1.2 centimeters e. 2 centimeters
d
The distribution of the time it takes for different people to solve a certain crossword puzzle is strongly skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is a. Normally distributed, with mean 30 and standard deviation 15. b. Skewed to the right, with mean 30 and standard deviation 15. c. Normally distributed, with mean 0 and standard deviation 1. d. Skewed to the right, with mean 0 and standard deviation 1. e. Skewed to the right, but the mean and standard deviation cannot be determined without more information.
d
The graph below shows how mothers of young children respond to the question, "How many times a week do you choose fast food as a dining option for your family?" What's wrong with this method of presenting information? a. This kind of data should always be presented in a pie chart. b. The vertical axis should be "number of responses," not "percentage of responses." c. The horizontal axis should be divided into more than three categories. d. Using proportionally-sized hamburgers exaggerates differences between responses. e. We don't know if the mothers who responded were thinking about dinner, or both lunch and dinner.
d
The mean birth weight of infants born at a certain hospital in the month of April was 128 oz. with a standard deviation of 10.2 oz. Which of the following is a correct interpretation of standard deviation? a. All the infants born in April weighed between 117.8 oz. and 138.2 oz. b. About half the infants born in April weighed between 117.8 oz. and 138.2 oz. c. The difference between the mean weight and the median weight of infants born in April was 10.2 oz. d. The distance between the weight of each infant born in April and the mean weight was, on average, about 10.2 oz. e. The mean weight of infants born in subsequent months is likely to be within 10.2 oz. of the mean weight in April.
d
The pie chart describes the distribution of state tree types for the 50 states in the United States. The category "Other" include all trees that are the state tree for two or fewer states. Which of the following conclusions can we draw from this chart? a. Some states have not designated a "state tree." b. The cottonwood is the state tree for 12 states. c. Taken together, oak, pine, and maple are the state trees for more than half the states. d. There are 10 states that have designated a pine as their state tree. e. There is no state that has designated the Eastern Red Cedar as its state tree.
d
The plot shown below is a Normal probability for a set of test scores. Which statement is true for these data? a. The data are clearly Normally distributed. b. The data are approximately Normally distributed. c. The data are clearly skewed to the left. d. The data are clearly skewed to the right. e. There is insufficient information to determine the shape of the distribution.
d
The population of the United States is aging, though less rapidly than in other developed countries. At right is a stemplot of the percents of residents aged 65 and older in each of the 50 states, according to the 2000 census. There are two outliers: Alaska has the lowest percent of older residents, and Florida has the highest. What is the percent for Florida? a. 13.8% b. 57% c. 176% d. 17.6% e. 5.7%
d
Which of the following is not true about all Normal distributions? a. The mean and median are equal b. The points at which the curvature changes from "up" to "down" (the points of inflection) are one standard deviation away from the mean on either side. c. About 2.5% of the values the variable takes on are more than two standard deviations above the mean. d. About 68% of the values of the variable are more than one standard deviation away from the mean. e. Z-scores of all the values of the variable have a mean of 0 and a standard deviation of 1.
d
Which statements below about least-squares regression are correct? I. Switching the explanatory and response variables will not change the least-squares regression line. II. The slope of the line is very sensitive to outliers with large residuals. III. A value of r2 close to 1 does not guarantee that the relationship between the variables is linear. a. Only I is correct. b. Only II is correct. c. Only III is correct. d. Both II and III are correct. e. All three statements—I, II, and III—are correct.
d
A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be -1.08. On the basis of this you would tell the college that a. the entrance exam is a good predictor of success. b. the exam is a poor predictor of success. c. students who do best on this exam will be poor students. d. students at this school are underachieving. e. the college should hire a new statistician.
e
A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat gave the following results: Predicted Calories = 97.1053 + 9.6525(Fat). Which of the following is false? a. It is estimated that for every additional gram of fat in the cereal, the number of calories increases by about 10. b. It is estimated that in cereals with no fat, the total amount of calories is about 97. c. If a cereal has 2 g of fat, then it is estimated that the total number of calories is about 116. d. The correlation between amount of fat and calories is positive. e. If one cereal has 140 calories and 5 g of fat. Its residual is about 5 calories.
e
A survey was done in the town of Mechanicsville to estimate the proportion of cars that are red and made by companies based in Japan. A random sample of 25 cars from a student parking lot at Lee-Davis High School was taken. Which of the following statements is not correct? a. This sample may not be representative of the cars in Mechanicsville because mainly students park at Lee-Davis High School. b. If the particular parking space is vacant, we can simply select another parking space at random because it is unlikely that a space being vacant is related to the color or manufacturer of the car. c. It would an error to simply select the first 25 parking spaces in the lot closest to the auditorium because there are a number of parking spaces there reserved for Drivers Ed vehicles, whose primary color is white. d. A different team doing the sampling independently would obtain different answers for their sample proportions. e. The results will be the same regardless of the time of day that the sample is taken.
e
All but one of the following statements contains an error. Which statement could be correct? a. There is a correlation of 0.54 between the position a football player plays and his weight. b. We found a correlation of r = -0.63 between gender and political party preference. c. The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second. d. We found a high correlation between the height and age of children: r = 1.12. e. The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.
e
At the beginning of the school year, a high-school teacher asks every student in her classes to fill out a survey that asks for their age, gender, the number of years they have lived at their current address, their favorite school subject, and whether they plan to go to college after high school. Which of the following best describes the variables that are being measured? a. four quantitative variables b. five quantitative variables c. two categorical variables and two quantitative variables d. two categorical variables and three quantitative variables e. three categorical variables and two quantitative variables
e
Below is a pie chart of how a randomly selected group of people described the cost of their heath insurance. Which of the following bar graphs is equivalent to the pie chart? (look at graph)
e
For the histogram below, what is the proper ordering of the mean and median? Note that the graph is NOT numerically precise—only the relative positions are important. a. I is the mean and II is the median. b. II is the median and III is the mean. c. I is the median and II is the mean. d. I is the mean and III is the median. e. II is the mean and III is the median.
e
If a distribution is skewed to the right, which of the following is true? a. The mean must be less than the median. b. The mean and median must be equal. c. The mean must be greater than the median. d. The mean is either equal to or less than the median, e. It's impossible to tell which of the above statements is true without seeing the data.
e
Rainwater was collected in water collectors at 30 different sites near an industrial complex and the amount of acidity (pH level) was measured. The data ranged from pH 2.6 to pH 6.3. The following stem plot of the data was constructed. (Look at Graph)
e
The 16th percentile of a Normally distributed variable has a value of 25 and the 97.5th percentile has a value of 40. Which of the following is the best estimate of the mean and standard deviation of the variable? a. Mean 32.5; Standard deviation 2.5 b. Mean 32.5; Standard deviation 5 c. Mean 32.5; Standard deviation 10 d. Mean 30; Standard deviation 2.5 e. Mean 30; Standard deviation 5
e
The median age of five people in a meeting is 30 years. One of the people, whose age is 50 years, leaves the room. The median age of the remaining four people in the room is a. 40 years. b. 30 years. c. 25 years. d. less than 30 years. e. Cannot be determined from the information given.
e
The weights of the male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a. About 50% of the male students have weights between 150 and 185 pounds. b. About 25% of female students have weights above 130 pounds. c. The median weight of male students is about 162 pounds. d. The mean weight of female students is about 120 pounds. e. The male students have less variability than the female students.
e
Which of the following best describes what s = 1218.65 represents in this setting? a. The standard deviation of the observed values of the response variable, injuries. b. The standard deviation of the predicted values of the response variable, injuries. c. The standard deviation of the observed values of the explanatory variable, PWC's in use. d. The average of the products of each standardized value for PWC and the corresponding standardized value for injuries. e. The standard deviation of the residuals.
e
You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. "Least-squares" refers to a. Minimizing the sum of the squares of the 25 houses' heating costs. b. Minimizing the sum of the squares of the number of rooms in each of the 25 houses. c. Minimizing the sum of the products of each house's actual heating costs and the predicted heating cost based on the regression equation. d. Minimizing the sum of the squares of the difference between each house's heating costs and number of rooms. e. Minimizing the sum of the squares of the residuals.
e