McFall AP Statistics Semester Exam

It's easy to measure the circumference of a tree's trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree's height, h, in feet from the circumference of its trunk, c, in inches. ln h= -1.2 +1.4(lnC). A lumberjack finds a tree with a circumference of 60". how tall does this model estimate the tree to be?

93 feet

5NS 11, 35, 61, 70, 79 380 took the test About how many students had scores between 35 and 61

95

A couple is planning an event out. They have a choice of 4 restaurants for dinner, 6 movies following dinner, and 4 coffee establishments for after the movie. How many different ways can they plan the evening if they choose one of each?

96

A researcher identified 100 men over forty who were not exercising and another 100 men over forty years with similar medical conditions who were exercising regularly. She followed all the men for several years to see if there was any difference between the two groups in the rate of heart attacks. This is a(n)

Prospective study

Of A-D, which is not a critical part of designing a good experiment?

Random selection of subjects.

A company sponsoring a new Internet search engine wants to collect data on the ease of using it. Which is the best way to collect the data?

Sample survey

You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list. In the situation of the two previous questions, the sample is

the 1347 teachers who mail back the questionnaire

The "average" income of American households in 1998 was either $38,885 or $51, 855, depending on whether we use the mean or median to measure center. We an say that

$51,885 is the mean because income distributions are skewed to the right.

How well does the number of beers a student drinks predict his or her blood alcohol content? The LSRL for predicting blood alcohol content from number of beers is y= -0.013 + 0.018x. Using this line, you predict that the BAC of a student who drinks 5 beers will be about

0.077

Using the standard normal distribution tables, what is the area under the standard normal curve corresponding to -0.5<Z<1.2

0.5764

Using the standard normal distribution tables, what is the area under the standard normal curve corresponding to Z>-1.22

0.8888

The auto insurance industry crashed some test vehicles into a cement barrier at speeds of 5 to 25 mph. They found a correlation of r=0.60 between speed and damage. If the speed at which a car hit the barrier is 1.5 standard deviations above the mean speed, we expect the damage to be ? the mean damage.

0.90 SD above

What is 0! ?

1

What is nCn

1

What is nP0

1

A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations given are mean x = 8.4, Sx = 2.1, mean y = 14.2, Sy = 3.8 and r = 0.86. What is the slope of the LSRL of number of service calls on number of copiers?

1.56

In how many ways can a committee consisting of 5 men and 6 women be formed from 8 men and 10 women

11760

Scores on the American College Testing (ACT) college entrance exam follow the normal distribution with mean 18 and standard deviation 6. Wayne's standard score on the ACT was -0.7 What was Wayne's actual ACT score?

13.8

Your statistics class has 30 students. You want to call an SRS of 5 students from your class to ask where they use a computer for the online exercises. You label the students 01, 02, ... 30. You enter the table of random digits at this line. Your SRS contains the students labeled

14, 03, 10, 22, 06

From a class of 12 boys and 10 girls a committee of 3 people is selected. How many different committees have at least 1 boy.

1420

North American area codes are three digit numbers. Before 1995, area codes had the following restrictions: the first digit could not be a 0 or an 8, the second digit was either 0 or 1, and the third digit was any number 1 through 9 inclusive. Under these rules, how many different area codes were possible?

144

A man has seven different pets and wishes to photograph them 3 at a time arranged in a line. How many different arrangements are possible?

210

The model square root of distance hat = 3.30 + 0.235(speed) can be used to predict the stopping distance in feet for a car traveling at a specific speed in mph. According to this model, about how much distance will a car going at 65 mph need to stop?

345.0 feet

If the heights of 99.7% of American men are between 5'0" and 7'0", what is your estimate of the standard deviation of height of American men?

4 inches

Katie wants to color a rainbow. She knows the seven colors that make up a rainbow, but can't remember the correct order. How many different ways could the colors be arranged assuming each color is only used once?

5040

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?

74%

A class of 14 students is made up of 6 girls and 8 boys. From this class, a group of 5 students is chosen to represent the class at a competition. Determine the number of different groups of 5 that can be formed if there must be 2 girls and 3 boys in each group.

840

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 variance is 225, 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?

875

How well does the number of beers a student drinks predict his or her blood alcohol content? The scatterplot shows

A moderately strong positive straight-line relationship between the number of beers and BAC

Suppose we fit a LSRL to a set of data. What is true if a plot shows a curved pattern?

A straight line is not a good fit for the data.

Which is true of the data shown in the histogram? I. The distribution is approximately symmetric II. The mean and median are approximately equal III. The median and IQR summarize the data better than the mean and standard deviation

I and II

Which statement about influential points is true?

I and II Removal of an influential point changes the regression line. Data points that are outliers in the horizontal direction are more likely to be outliers in the vertical direction..

An instructor has 5 sections of a course: A, B, C, D, and E. She wants to randomly select three sections for a special teaching evaluation. She labels the classes as follows: A=... E=5. Which classes did she select?

A, D, and E

Among a dozen eggs, three are rotten. A cookie recipe calls for two eggs; they'll be selected randomly from that dozen. Which plan could be used to simulate the number of rotten eggs that night be chosen?

I only Let 00, 01, and 02 represent the rotten eggs...

Which of the following statements is/are true?

II and III only Scatterplots require that both variables be quantitative and every LSRL passes through (x bar, y bar)

Suppose that a Normal model describes fuel economy (mile per gallon) for automobiles and that Saturn has a standardized score (z-score) of +2.2. This means that Saturns

Achieve fuel economy that is 2.2 standard deviations better than the mean

A description of different houses on the market includes 4 variables. Which of these variables is quantitative?

All of the above

If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)?

B will decrease, R will increase

Your score on the statistics final exam is at the 70th percentile of scores for the class. Your score lies

Between the median and the third quartile

In an experiment the primary purpose of blinding is to reduce...

Bias

Placebos are a tool for

Blinding

Which of these statements about the standard deviation is true?

Both A and B, but not C (s is always 0 or positive and s should be used to measure spread only when the mean is used to measure center, not that it has no units)

Wayne tells Garth, "There is a correlation of r=1.51 between the gender of factory workers and their salary." Wayne's statement makes no sense because

Both b and c (gender is a categorical variable, the correlation can't be larger than 1)

The change in scales makes it hard to compare scores on the 1994 math SAT (mean 470, standard deviation 110) and the 1996 math SAT (mean 500, standard deviation 100). Jane took the SAT in 1994 and scored 500. Her sister Colleen took the SAT in 1996 and scored 520. Who did better on the exam, and how can you tell?

Jane-- her standard score is higher than Colleen's

We wish to compare the average ages of math and science teachers at your high school. Which is the best way to collect the data?

Census

A survey records many variables of interest to the researchers conducting the survey. Which of the following variables, from a survey conducted by the US postal service, is categorical?

County of residence

A researcher wants to compare the performance of three types of pain relievers in volunteers suffering from arthritis. Because people of different ages may react differently to medication, the subjects are split into two groups: under 60 and over 60. Subjects in each group are randomly assigned to take one of the medications. Twenty minutes later they rate their levels of pain. This experiment

Has one factor (medication) and is blocked by age.

If removing an observation from a data set would have a marked change on the position of the LSRL fit to the data, what is the point called?

Influential

If a data set A of (x,y) data has correlation coefficient of r=0.65, and a second data set B has correlation r= -0.65, then

Neither A nor B has a strong linear association

A factory has 20 assembly lies producing a popular toy. To inspect a representative sample of 100 toys, quality control staff randomly selected 5 toys from each line's output. Was this a simple random sample?

No, because not all combinations of 100 toys could have been chosen.

Can watching a movie temporarily raise your pulse rate? Researchers have 50 volunteers check their pulse rates. Then they watch an action film, after which they check their pulse rates once more. Which aspect of experimentation is present in this research?

None of these.

How well does the number of beers a student drinks predict his or her blood alcohol content? The LSRL for predicting blood alcohol content from number of beers is y= -0.013 + 0.018x. The slope 0.018 of this line tells us that

On the average, BAC increases by 0.018 for each additional beer a student drinks

A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat gave the following results: Calories + 97.1053 + 9.6525(Fat). Which of the following is FALSE?

One cereal has 140 calories and 5 g of fat. Its residual is about 5 cal.

5NS 11, 35, 61, 70, 79 380 took the test What does the five-number summary suggest about the skewness of the distribution of scores?

Skewed to the left

There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by their height = 50.3 + 6.01(age) where height is measured in centimeters and age in years. Which of the following is not correct?

The estimated intercept is 50.3 cm, which implies that children reach this height when they are 50.3/6.01 = 8.4 years old

Which of the following is likely to have a mean that is smaller than the median?

The scores of students out of 100 points on a very easy exam in which most score perfectly, but a few do very poorly

For the distribution of 380 exam scores,

The median is very likely to be greater than the mean

The standard deviation is a measure of

The spread of variability of a distribution

Which of the following variables would most likely follow a Normal model?

Weights of adult male elephants

You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list. In all 1347 teachers return the questionnaire. In this situation, the population is

all American school teachers

You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list. In the situation of the previous question, the sampling frame is

all members of the National Education Association

In a study of 1991 model cars, a researcher found that the fraction of the variation in the price of cars was explained by the LSR on horsepower was about 0.64. For the cars in this study, the correlation between price of the car and its horsepower was found to be positive. The actual value of the correlation is

is 0.80

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The overall mean number of hours worked...

is 7.2

What can we say about the relationship between a correlation r and the slope b of the LSRL for the same set of data?

r and b always have the same sign

How well does the number of beers a student drinks predict his or her blood alcohol content? A plausible value between number of beers and blood alcohol content, based on the scatterplot is

r=0.9