# AP Stats Midterm

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### 1. In an experiment, an observed effect so large that it would rarely occur by chance is called

statistically significant

### 2. Which statements below about the least-squares regression line 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

Both II and III are correct

### 3. 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 y=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

The actual relationship between salary raises and performance rating is linear

1.2 centimeters

### 5. 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

63 inches to 73 inches

### 6. 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

Skewed to the right, with mean 0 and standard deviation 1

### 7. What is the distribution of values taken by a statistic in all possible samples of the same size from the same population called

The sampling distribution of the statistic

### 8. The weights of the male and female students in a class are summarized in the following boxplot. Which of the following is NOT correct

The male students have less variability than the female students

\$11,450

### 10. A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting

Y has a binomial distribution with n=40 observations and probability of success p=0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected

### 11. 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

The distribution is skewed right

### 12. You take a sample of size 25 from a very large population in which the true proportion is p=0.1, thus violating the condition that np>10 and n(1-p)>10. Which statement below best describes what you know about the sampling distribution of p

Mean=0.1; S(x)=(0.1*0.9)/25)^.5; the distribution is not approximately Normal

### 13. 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 matched pairs experiment

16

### 15. A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is \$0.25, and it costs him \$5.00 per day to maintain the machine and rent the space for it. What are the mean and standard deviation for Y=the profit he earns from this machine in a randomly-selected week

Mean=26.25, standard deviation=\$1.75

### 16. Which of these variables is least likely to have a normal distribution

Annual income for all 150 employees at a local high school

0.526

### 18. A student investigating study habits asks a simple random sample of 16 students at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are mean=45 minutes and s(x)=15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student's sample

mean=45, s(x)=3.75, shape of distribution unknown

### 19. A public opinion poll in Ohio wants to determine whether or not registered voters in the state approved of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a

stratified random sample

### 20. 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); 5, 7, 12, bdl, 10, 8, bdl, 20, 6

The median lead level in the water is 7 ppm

0.896

### 22. 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

on average, the number of copies made each day was about 24 copies per day away from the mean, 258

(70,75), 9.19%

### 24. Which of the following random variables is geometric

The number of digits I will read beginning at a randomly selected starting point in a table of random digits until I find a 7

### 25. 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

the mean would increase by \$5,000 and the median would not change

mean=30, s(x)=5

### 27. If a distribution is skewed to the right, which of the following is true

the mean must not be greater than the median

### 28. The sampling distribution of a statistic is

the distribution of values taken by a statistic in all possible samples of the same sample size from the same population

95

cluster sample

### 31. The best statistic for estimating a parameter has which of the following characteristics

low bias, low variability

nonresponse bias

0.0228

### 34. 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

minimizing the sum of the squares of the residuals

0.147

0.591

a block design

### 38. Control groups are used in experiments in order to

control the effects of outside variables on the outcome

### 39. Select a random integer from -100 to 100. Which of the following pairs of events are mutually exclusive (disjoint)

A-the number is above 50 and B-the number is less than 20

### 40. 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 y=410.54+67.3x. Which of the following about the circled point is false

removing the student's data point would increase the slope of the least-squares line

95.5

I and II only

0.6352

3

875

75%

I,II, and III

III only

I,III.

I and II

### 51. Here are the IQ test scores of 10 randomly chosen fifth-grade students-145,139,126,122,125,130,96,110,118,118. To make a stemplot of these scores, you would use as stems

09,10,11,12,13, and 14.

600

19

34.5%

0.030

0.75

### 57. According to a 1990 census, those states with an above-average number of people X, who fail to complete high school tend to have an above average number of infant deaths, Y. In other words, there is a positive association between X and Y. The most plausible explanation for this is

Lurking variables are probably present. For example, states with large populations may have both larger numbers of people who don't complete high school and more infant deaths.

### 58. The probability of any outcome of a random phenomena is

the proportion of times the outcome occurs in a very long series of repetitions

0.80.

### 60. A double-blind experiment was conducted to evaluate the effectiveness of the Salk polio vaccine. The purpose of keeping the diagnosing physicians ignorant of the treatment status of the experimental subjects was to

eliminate the possible source of bias

0.160

### 62. Use Scenario 5-13. You select one student from the group at random. Which of the following statements is true about the events "Typically walks to school" and Junior

the events are not mutually exclusive but they are independent

statistic

### 64. 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

gas mileage is a response variable, and you expect to find a negative association

### 65. 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

the explanatory variable is parents' income, and you expect to see a positive association

### 66. Which of the following is a true statement

an important difference between binomial and geometric random variables is that there is a fixed number of in a binomial setting, and the number of trials varies in a geometric setting

### 67. The reason that blocking (in a randomized block design) is sometimes used in experimentations is to

reduce variability arising from random assignment

1.56

### 69. The central limit theorem refers to which of the following characteristics of the sampling distribution of the sample mean

regardless of the shape of the population's distribution, the sampling distribution of the sample mean from sufficiently large samples will be approximately normally distributed

0.44

### 71. If A=result of a single roll of a six-sided die and B=result of a single roll of an 8-sided die, then meanA=3.5, S(a)=1.71, meanB=4.5, and S(b)=2.29. If D=the difference B-A, then which of the following is true

meanD=1, S(d)=sq root(1.71)²+(2.29)²

0.2

### 73. 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 three storage times. The treatment, experimental unit, and response are respectively

a specific storage time, a fruit pack, amount of vitamin C

### 74. A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she's been authorized to repave for the study. She decides to carry out a matched-pairs experiment. Which of the following is the best way for her to carry out the randomization for this study

let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement

### 75. The variance of sum of two random variables X and Y is

(s(x)2 + (s(y)2, but only if X and Y are independent

### 76. We say that the design of a study is biased if which of the following is true

certain outcomes are systematically favored

### 77. Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

(10/3)(1/8)^3(7/8)^7

0.0668.

### 79. The mean speed of vehicles in the "cars only" lane of the New Jersey turnpike is 68 miles per hour. The mean speed of vehicles in the "any vehicle" lane 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

It could be any number between 64 and 68 miles per hour

### 80. If your score on the test is at the 60th percentile, you know that your score lies

between the median and the third quartile

998

### 82. Which of the following is a method for improving the accuracy of a sample

use larger sample sizes

\$3.50

unbiased

0.1551

P(A or B)=1.0

### 87. 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 tell you about the linear model

the curved pattern in the residual plot suggests that the linear model is not appropriate

### 88. An agricultural economist says that the correlation between corn prices and soybean prices is r=0.7. This means that

when corn prices are above average, soybean prices also tend to be above average

a block design

### 90. A recent survey by a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided "are the most likely to know how important universities are to the Canadian economy." The main problem with using these results to draw conclusions about the general public's perception is

lack of random selection

0.2119

\$255

### 93. At a school with 600 students, 25% of them walk to school each day. If we choose a random sample of 40 students from the school, is it appropriate to model the number of students in our sample who walk to school with a binomial distribution where n=40 and p=0.25

Yes, because the sample size is less than 10% of the population size

### 94. 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

The report gives only the mean. This does not imply that all participants in the study lost 10.4 pounds or even lost weight. Your friend's experience does not necessarily contradict the study results.

### 95. 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 points are important

I is the mean and II is the median

74%

79.11

### 98. 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 the chart

There are 10 states that have designated pine as their state tree

### 99. A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. This kind of sample is called a

stratified random sample

### 100. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the mean and standard deviation of the number of students in the sample who have experienced math anxiety is

mean=2, s(x)=1.265

III and IV

### 102. 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 can conclude

nothing, because there is no control group for comparison

### 103. If we took an SRS of 1700 people from California (population 34 million) and a SRS of 1000 people from Detroit (population 1 million) which sampling distribution would have the smaller standard deviation

California, because the sample size (1700) is larger than for Detroit (1000)

### 104. A friend has placed a large number of plastic disks in a hat and invited you to select one at random. He informs you that they have numbers of them, and that one of the following is the probability model for the number on the disk you have chosen. Which one is it

the one where the probabilities add up to 1

### 105. Use Scenario 3-14. The least-squares regression line is the line that

minimizes the sum of the squared residuals between the actual yield and the predicted yield

0.25

### 107. 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-11362 35692 96237 90842

households 11,36, 23, 08, 42

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