AP Stats Midterm Review

Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists. Round to three decimal places.

r=​0.983; a linear relation exists

Describe the shape of the histogram. The data set consists of the ages of 20 household stereo systems that were randomly selected from a neighborhood.

roughly symmetric

The accompanying boxplot was constructed in Excel for the amount of soda that was poured by a filling machine into​ 12-ounce soda cans at a local bottling company. Based on the information given in the​ boxplot, what shape do you believe the data to​ have?

skewed to the left

Find the equation of the regression line for the given data. Round values to the nearest thousandth.

y=2.097x−0.552

A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the​ drought's effect on the size of his trees. To decide whether the growth of the trees has been​ retarded, the farmer decides to take a sample of the heights of 25 trees and obtains the following results​ (recorded in​ inches). The tree farmer feels the normal height of a tree that was unaffected by the drought would be 65 inches. Find the​ z-score for a tree that is 65 inches tall.

z=0.84

Classify the variable as qualitative or quantitative. the temperatures of cups of coffee served at a restaurant

Quantitative

The regression line for the given data is y=−0.206x+2.097. Determine the residual of a data point for which x=22 and y=negative 5−5.

-6.685

The events A and B are mutually exclusive. If P(A)equals=0.20 and P(B)=0.6, what is​ P(A and​ B)?

0

At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 102 miles per hour​ (mph) and the standard deviation of the serve speeds was 12 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bell shaped. What proportion of the​ player's serves are expected to be between 114 mph and 126 mph? Round to four decimal places.

0.1350

Suppose that M and N are two​ events, P(M)=0.2222​, ​P(N)=0.077​, and​ P(M and ​N)=0.044. What is P(Upper M vertical lineM​N)? Round to three decimal places as needed.

0.571

A manager wishes to determine the relationship between the number of years the​ manager's sales representatives have been with the company and their average monthly sales​ (in thousands of​ dollars). Calculate the linear correlation coefficient. Round to three decimal places.

0.632

A​ fast-food restaurant chain with 700 outlets in the United States describes the geographic location of its restaurants with the accompanying table of percentages. A restaurant is to be chosen at random from the 700 to test market a new style of chicken. Given that the restaurant is located in the eastern United​ States, what is the probability it is located in a city with a population of at least​ 10,000? Give your answer as a decimal rounded to the nearest thousandth.

0.750

A​ fast-food restaurant chain with 700 outlets in a certain country describes the geographic location of its restaurants with the accompanying table of percentages. A restaurant is to be chosen at random from the 700 to test market a new style of chicken. Given that the restaurant is located in the eastern part of the​ country, what is the probability it is located in a city with a population of at least​ 10,000? Round to the nearest thousandth.

0.810

Find the sample standard deviation. Round to one decimal place. 10, 11, 12​, 13​, 14

1.6

A single​ 6-sided die is rolled twice. The set of 36 equally likely outcomes is​ {(1,1), (1,2),​ (1,3), (1,4), (1,5), (1,6), (2,1),(2,2), ​(2,3), (2,4),​ (2,5), (2,6),​ (3,1), (3,2),​ (3,3), (3,4),​ (3,5), (3,6),​ (4,1), (4,2),​ (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), ​(5,3), (5,4),​ (5,5), (5,6),​ (6,1), (6,2),​ (6,3), (6,4),​ (6,5), (6,6)}. Find the probability of getting two numbers whose sum is greater than 9.

1/6

In how many ways can a committee of three men and four women be formed from a group of 12 men and 12 women?

108900

In a contest in which 9 contestants are​ entered, in how many ways can the 5 distinct prizes be​ awarded?

15,120

For the following​ data, approximate the mean number of emails received per day.

16.1

A group of 79 students were asked how far they commute to work from home each time they go to work from home. The results are given to the right. Determine the first quartile.

4 mi

Retailers are always interested in determining why a customer selected their store to make a purchase. A sporting goods retailer conducted a customer survey to determine why its customers shopped at the store. The results are shown in the accompanying bar graph. What percentage of the customers responded that the merchandise was the reason they shopped at the​ store? Round to the nearest whole percent.

43%

Determine the number of classes in the frequency table below.

5

The graph to the right is an ogive of scores on a math test. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Use the ogive to approximate the test score that corresponds to the 30th percentile.

56

Evaluate the factorial expression. (600!/599!)

600

Two​ companies, A and​ B, package and market a chemical substance and claim 0.15 of the total weight of the substance is sodium.​ However, a careful survey of​ 4,000 packages​ (half from each​ company) indicates that the proportion varies around​ 0.15, with the results shown below. Find the percentage of all chemical B packages that contain a sodium total weight proportion above 0.150.

80%

A student receives test scores of​ 62, 83, and 91. The​ student's term project score is 88 and her homework score is 76. Each test is worth​ 20% of the final​ grade, the term project is​ 25% of the final​ grade, and the homework grade is​ 15% of the final grade. What is the​ student's mean score in the​ class?

80.6

A license plate is to consist of 3 letters followed by 4 digits. Determine the number of different license plates possible if the first letter must be an​ K, L, or M and repetition of letters and numbers is not permitted.

9,072,000

The following data represent the bachelor degrees of​ CEO's at area small businesses. Determine the mode degree.

Business 47

_______ is/are a method of interpreting the standard deviation that applies to any data​ set, regardless of the shape of the distribution.

Chebyshev's Rule

Determine whether the following statement is true or false. Mutually exclusive events are always independent.

False

Civil engineers often use the​ straight-line equation, y= 0β0+β1​x, to model the relationship between the mean shear strength of masonry joints and precompression​ stress, x. To test this​ theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure​ (called the shear​ strength) was recorded. The stress results for n=7 triplet tests is shown in the accompanying table followed by a printout of the regression analysis. Give a practical interpretation of the estimate of the slope of the least squares line. Round to three decimal places if needed.

For every 1 ton increase in precompression​ stress, the shear strength of the joint is estimated to increase by 0.987 tons.

The pie chart shows the percentage of votes received by each candidate in the student council presidential election.

Matt 16%

The chart to the right shows the percentage of people in a questionnaire who bought or leased the listed car models and were very satisfied with the experience. With which model was the greatest percentage​ satisfied? Estimate the empirical probability that a person with this model is very satisfied with the experience. Express the answer as a fraction with a denominator of 100. Model A ​ 81% Model B ​ 79% Model C ​ 73% Model D ​ 61% Model E ​ 59% Model F ​ 57%

Model A; (81/100)

A medical researcher wishes to determine if there is a relationship between the number of prescriptions written by pediatricians and the ages of the children for whom the prescriptions are written. She surveys all the pediatricians in a geographical region to collect her data. What is the response​ variable?

Number of prescriptions written

A professor wants to arrange his books on a shelf. He has 30 books and only space on the shelf for 20 of them. How many different​ 20-book arrangements can he make using the 30​ books? This is an example of a problem that can be solved using which​ method?

Permutations

Which of the following is not true of​ statistics?

Statistics is used to answer questions with​ 100% certainty.

The city council of a small town needs to determine if the​ town's residents will support the building of a new library. The council decides to conduct a survey of a sample of the​ town's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the​ town's residents?

Survey a random sample of persons within each neighborhood of the town.

What is the difference between a bar chart and a​ histogram?

The bars on a bar chart do not touch while the bars of a histogram do touch.

Construct a frequency distribution for the data using five classes. Describe the shape of the distribution.

The distribution is uniform.

Which of the following sentences is a description of the median of a data set for a​ variable?

The median is the data value that lies in the middle of the data when the data is arranged in ascending order.

Determine what type of observational study is described. Explain. A researcher wanted to determine whether colon cancer was associated with eating meat. He selected a sample of 500 men with colon cancer and an equal number of men without colon cancer. The two groups were similar in terms of​ age, occupation,​ income, and exercise levels. Histories on the amount of meat consumed over the previous twenty years were obtained for all men. The total amount of meat that each man eaten in the previous twenty years was estimated. The meat consumption was compared for the two groups.

The observational study is a retrospective study because individuals are asked to look back in time.

Make a scatter diagram for the data. Use the scatter diagram to describe​ how, if at​ all, the variables are related.

The variables appear to be​ positively, linearly related.

Explain what is misleading about the graphic.

The vertical scale does not begin at zero.

The following data represents a random sample of 15 complaints registered with the customer service department of a store. Determine the median complaint.

There is no median complaint.

A frequency polygon always begins and ends with a frequency of zero.

True

The sum of all the relative frequencies of a distribution will always add up to 1.

True, neglecting small rounding errors

An ogive is a graph that represents cumulative frequencies or cumulative relative frequencies. What are the points labeled on the horizontal​ axis?

Upper class limits

Fill in the blank below. ​_______ is a condition applied to the experimental units involved in an experiment.

a treatment

A researcher wants to study the effects of advertising by female models upon high school boys in small Midwestern towns. The research methodology calls for selecting several small Midwestern towns that have high schools. What is the frame for this​ study?

all high school boys from small Midwestern towns

A drug company wanted to test a new acneacne medication. The researchers found 7700 adults aged​ 25-35 and randomly assigned them to one of two groups. The first group received the new​ drug, while the second received a placebo. After one month of​ treatment, the percentage of each group whose acneacne symptoms decreased was recorded and compared. What type of experimental design is​ this?

completely randomized design

Identify the type of sampling used. Based on 11 comma 00011,000 responses from 32 comma 00032,000 questionnaires sent to all its​ members, a major medical association estimated that the annual salary of its members was ​$95 comma 50095,500 per year. What sampling technique was​ used?

convenience

Determine whether the quantitative variable is discrete or continuous. The number of violent crimes committed in a city on a given day in a random sample of 110110 days

discrete

Determine whether the study depicts an observational study or an experiment. A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 23 people to a treatment group and 23 to a placebo group. The treatment group receives a medication over a period of three months and the placebo group receives a placebo over the same time frame. At the end of three months the​ patients' symptoms are evaluated.

experiment

Determine the level of measurement of the variable. the year of manufacture of a car

interval

For the​ stem-and-leaf plot​ below, what are the maximum and minimum​ entries?

max=477​; min=12

Find the population mean or sample mean as indicated. ​Population: 5​, 10, 2​, 11​, 13​, 19

mu=10

Determine whether the underlined value is a parameter or a statistic. In a survey conducted in a certain​ town, Modifying 21 % with underline21% of adult respondents reported that they had been involved in at least one car accident in the past ten years.

statistic

A farmer wishes to test the effects of a new fertilizer on her tomato yield. She has four​ equal-sized plots of land. One plot has sandy​ soil, one has rocky​ soil, one has​ clay-rich soil, and one has average soil. She divides each of the four plots into three​ equal-sized portions and randomly labels them​ A, B, and C. The four A portions of land are treated with her old​ fertilizer, the four B portions of land are treated with the new​ fertilizer, and the four C portions of land are treated with no fertilizer. At harvest​ time, the tomato yield is recorded for each section of land. Identify the experimental units.

the tomato plants on the various plots of land

A probability experiment is conducted in which the sample space of the experiment is Upper S= { 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 }.S={4,5,6,7,8,9,10,11,12,13,14}. Let event A={7,8,9,10,11}. Assume that each outcome is equally likely. List the outcomes in Ac. Find P(Ac​).

{4​,5​,6​,12​,13​,14​}; (6/11)

Which of the following probabilities for the sample points​ A, B, and C could be true if​ A, B, and C are the only sample points in an​ experiment?

​P(A)=​0, P(B)=​1/2, P(C)=1/2

A probability experiment is conducted in which the sample space of the experiment is Upper S equals { 1, 2, 3, 4, 5, 6, 7, 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 }.S={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. Let event Upper A equals { 3 comma 4 comma 5 comma 6 }A={3,4,5,6} and event Upper B equals { 11 comma 12 comma 13 }.B={11,12,13}. Assume that each outcome is equally likely. List the outcomes in A and B. Are A and B mutually​ exclusive?

​{}; yes