Ms. Horstman AP Statistics Midterm Review
The histogram below shows the closing price of a stock on 50 days. In which range does the first quartile lie?
A) 0 and 10
The equation of the least squares regression line for the points on the scatterplot below is y=1.3 + 0.73x. What is the residual for the point (4,7)?
A) 2.78
The army reports that the distribution of head circumferences among soldiers is approximately normal with mean 22.8 inches and standard deviation 1.1 inches. The army plans to provide custom made helmets for soldiers whose head circumference falls in the top 1% of the distribution. What minimum head circumference is required (in inches) to fall in the top 1%?
A) 25.36
The five number summary for a one variable dataset is {5, 18, 20, 40, 75}. If you wanted to construct a modified boxplot for the dataset {that is, one that would show outliers if there are any). what would be the maximum possible length of the right side "whiskey""
A) 33
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachel is at the 99th percentile for adult women, then heir height,t in inches, is closet to
A) 70 inches
A professor scaled (curved) the scores on an exam by multiplying the student's raw score by 1.2, then adding 15 points. If the mean and standard devotion of the scores before the curve were 51 and 5, respectively, then the mean and standard deviation of the scaled scares are respectively:
A) 76.2 and 6
The army reports that the distribution of head circumference among soldiers is approximately normal with mean 22.8 inches and standard deviation 1.1 inches. What percent of soldiers have head circumference between 20 inches and 25 inches?
A) 97.18%
In the scatterplot of y verses x below. the least squares regression line is superimposed on the plot. Which of the following points have the largest residual?
A) A
A student organization wants to assess the attitudes of students toward a proposed changing the hours that the library is open. They randomly select 50 freshman, 50 sophomores, 50 juniors, and 50 seniors. The situation described is
A) A stratified random sample
In the northern US, schools are often closed during severe snowstorms. These missed days must be made up at the end of the school year. The following histogram shows the number of days missed per year for a particular school district from the past 75 years. Which of the following should be used to describe the center of the distribution?
A) Median, because the distribution is skewed
Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class?
A) She scored about equally well on both exams
One advantage of using a stem-and-leaf plot rather than a histogram is that the stem-and-lea plot
A) Shows all of the data on the graph
Which of the following is the best estimate of the standard deviation of the distribution shown in the figure below?
B) 10
There is a linear relationship between the number of chirps made by the striped cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model y=25.2+3.3x for 9<x<25 where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
B) 16.5 degrees F
The five number summary for scores on a statistics exam is 35, 68, 77, 83, 97. In all, 196 students took the test. About how many had scores between 77 and 83?
B) 49
The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. What percent of young men are taller than 6 feet?
B) 5.5
The heights of American men aged 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5 inches. Only about 5% of young men have heights outside the range
B) 63 inches to 73 inches
Gina's doctor told her that the standerdized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.60. Which of the following is the best interpretation of this standerdized score?
B) Gina's systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age
A substitute teacher was asked to keep track of how long it took her to get to her assigned school each morning. Here is a stem plot of the data. Would you expect the mean to be higher or lower than the median>
B) Higher, because the data are skewed to the right
Suppose that the distribution of a set of scores has a mean of 47 and standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of the new score?
B) Mean=51 and SD=14
A company wanted to determine the health care costs of its employees. A sample of 25 employees was interviews and their medical expenses for the previous year were determined. Later the company discover that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error. the corrected amount was still greater than or equal to any other medical expenses in the sample. Which of the following sample statistics must have remained the same after the correction was made?
B) Median
A large elementary school has 15 classrooms, with 24 children in each classroom. Each of the 15 teachers selects 2 children from his or her classroom to be in the sample by numbering the children from 1 to 24, then using a random digit table to select two different random numbers between 01 and 24. The 2 children with those numbers are in the sample. Did this procedure give a simple random sample of 20 children form the elementary school?
B) No, because not all possible groups of 30 children had the same chance of being chosen
At a college the scores on the chemistry final exam are approximately of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scores 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?
B) The student did equally well in each course
The man way to protect against confounding is to
B) Use a randomized comparative study
The scores on a statistics exam are strongly skewed to the right with outliers. So it is best to describe the distribution by reporting
B) the five number summary
Jason appears to be growing slowly as a toddler. His height between 18 and 30 months of age increases as follows - Age (months) 18 21 24 27 30 Height (cm) 76.5 78.7 82.0 84.8 86.0 The least squared regression line of his height on age is
B) y=61.5+ 0.837x
One of the values in a normal distribution is 43 and its z-score is 1.65. If the mean of the distribution is 40, what is the standard deviation of the distribution?
C) 1.82
A professor teaches two statistics classes. The morning class has 25 students and their average on the first test was 82. The evening class had 15 students and their average on the same test was 74. What is the average on this test if the professor combines the scores for both classes?
C) 79
You are told that your score on an examination was at the 65th percentile. Your score was
C) Between the median and the third quartile
We say that the design of a study is biased if which of the following is true?
C) Certain outcomes are systemically favored
A study reports a correlation of r=-0.71 between family income in dollars and the number of pounds of soft margarine the family consumes in a year. You conclude that
C) Higher income families consume less soft margarine than do lower income families
Which of the following are true statements? I. Voluntary response samples often under-represent people with strong opinions II. Convenience samples often lead to under-coverage bias III. Questionnaires with non-neutral wording are likely to have response bias
C) II and III
The boxplots below summarize two data sets, A and B. Which of the following must be true? I. Set A contains more data than Set . II. The box plot of Set A contains more data than the box of Set B. III. The data in Set A have a larger range than the data in Set B.
C) III only
When the estrogen blocking drug tamoxifen was first introduced to treat breast cancer, there was concern that it would cause osteoporosis as a side effect. To test this concern ,cancer subjects were randomly selected and given tamoxifen, and their bone density was measured before and after treatment. Which of the following is a true statement? I. This study was an observational study II. This study was a sample survey of randomly selected cancer statements III. This study was an experiment in which the subjects were used as their own controls.
C) III only
Out of a large shipment of fuses received from a new supplier, a manufacturer decides to accept his particular shipment. In arriving at this decision the manufacture interpreted
C) The fuses tested as a sample and the shipment as a population
The mean age (positive integers) of all 19 students in a statistics class is 17.5 years. A 12 year old (additional) student enrolls. What is the new approximate mean age of the students in the class?
D) 17.2
The median age (positive integers) of all 19 students in a statistics class is 18 years old. A 17 year old student withdraws form the class and a 12 year old enrolls. What is the new approximate median age of the students in the class?
D) 18
The 1992 NAEP Trial State Assessment calculated a state-by-state average mathematics proficiency score for students in the eighth grade. The resulting boxplot is shown below. Which of the following statements are true? I. The state score 273 has a percentile rank of 75 II. The mean state score is 267 III. The lowest state score is 246
D) I and III only
If the largest value of a data set is doubled, which of the following is false?
D) The interquartile range increases
The scores of male (M) and female (F) students on a statistics exam are displayed in the following boxplots. The pluses indicate the location of the means.
D) The scores of the males have a higher variability than the scores of the females
The figure below shows a cumulative relative frequency histogram of 40 scores on a est given in an AP Statistics class. Which of the following conclusions can be made from the graph?
D) There is less variability in the upper 20 test scores than in the lower 20 test scores
Two events are said to be mutually exclusive (disjoint) if
D) They do not contain any outcomes in common
For which of the following distributions is the mean less than the median?
E)
The correlation between two scores X and Y equals 0.8. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be
E) 0.8
A set of 5,000 scores on a college readiness exam are known to be approximately normally distributed with mean 72 and standard deviation 6. To the nearest integer value. how many scores are there between 63 and 75?
E) 3,123
The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six bones with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this?
E) Cluster random sample
The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the following statements about these two data sets CANNOT be justified.
E) Data set I has more data points than data set II
The relation between the selling price of a car (in $1000) and its age (in years) is estimated from a random sample of cars of a specific model. Based on the collected data, the least squares regression line is (Selling price) = 15.9 -0.983(age) Which of the following can we conclude from this equation?
E) For ever year the car gets older, the selling price drops by approximately $983
Which of the following statements is (are) true? I. The median is resistant to extreme values II. The mean is resistant to extreme values III. The standard deviation is resistant to extreme values
E) I only
Anthropologists must often estimate from human remains how tall the person was when alive. Tod o this we study how overall height can be predicted from the length of a leg bone in a group of 36 living males. The data show that the bone lengths have mean 45.9 centimeters and standard deviation 4.20 cm, overall height for the same men has mean 172.7 cm and standard deviation 8.14 cm, and the correlation between bone length and height is 0.914. About what percent of the observed variation in the heights of the length of the leg bone?
E) None of these
Twenty men and 20 women with high blood pressure were subjects in an experiment to determine the effectiveness of a new drug in lowering blood pressure. Ten of the 20 men and 10 to the 20 women were chosen at random to receive the new drug. The remaining 10 en and 10 women received a placebo. The change in blood pressure was measured for each subject. The design of this experiment is
E) Randomized block, blocked by gender
As shown below, a least-squares regression line has been fitted to the winning percentages for a local sports team in each of the years 1983 through 1995. The percentages for the 1996 season was then plotted (as circled below). Which of the following statements correctly describes how the value for the 1996 season will change the appearance of the least-squares regression line and the correlation coefficient if a new least-square regression line is fitted to the 1983 through 1996 data?
E) The 1996 point will make the least-squares regression line steeper and the correlation coefficient weaker.
Exercise physiologists are investigating the relationship between lean body mass ( in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. Based on the computer output above, which of the following is the equation of the least squares regression line?
E) rate=264.0+22.563mass
