Statistics Chapters 1-3
Variance
1. Find the Mean 2. For each number, subtract the mean and square the result 3. Work out the mean for those square differences (amount of numbers-1) Example: 1, 2, 2, 3, 5 Mean- 2.6 (1-2.6)^2 + (2-2.6)^2 + (2-2.6)^2 + (3-2.6)^2 + (5-2.6)^2 (2.56+0.36+0.36+0.16+5.76)/(5-1) Variance= 2.3
Simple random sampling A. reduces bias resulting from poorly worded questions. B. guarantees valid results. C. reduces bias resulting from the behavior of the interviewer. D. offsets bias resulting from undercoverage and nonresponse. E. None of the above.
E. None of the above.
- Lily's travel time from her dorm to the student union at the University of Virginia - Number of cars in a parking lot
Interval
A sample of 200 professional football players is taken to estimate the mean weight of all adult males. Is this study
NON-REPRESENTATIVE
A sample of 300 dentists from Seattle is taken to estimate the median income of all Seattle residents. Is this study
NON-REPRESENTATIVE
A simple random sample of 10 men over the age 18 is taken to estimate the mean height of all adult males. Is this study
NON-REPRESENTATIVE
A telephone survey of 1000 registered voters is conducted during the day in order to determine the chances of a certain candidate winning an election. Is this study
NON-REPRESENTATIVE
Using a sample of 40 patients from a local hospital, researchers measured cholesterol level in an attempt to estimate the mean cholesterol level of U.S. citizens.
NON-REPRESENTATIVE
- Heidi's favorite brand of tennis balls - Your marital status
Nominal
- The occupation of your neighbors - The marital status of your coworkers
QUALITATIVE
- The amount of bacteria on a piece of moldy bread - Your college GPA
QUANTITATIVE
A simple random sample of 30 residents from Seattle is taken to estimate the median income of all Seattle residents. Is this study
REPRESENTATIVE
A simple random sample of 400 U.S. citizens is taken in order to estimate the mean cholesterol level of U.S. citizens. Is this study
REPRESENTATIVE
A simple random sample of men over age 18 is taken to estimate the mean weight of all adult males. Is this study
REPRESENTATIVE
A simple random sample of voters is taken in order to determine the chances of a certain candidate winning an election. Is this study
REPRESENTATIVE
Qualitative data
Data obtained from a nonnumerically valued variable
The ratio of the frequency of a class to the total number of observations
relative frequency
a tabular summary of a set data showing the fraction of the total number items in several classes is a:
relative frequency distribution
Discrete, quantitative data
Data obtained by observing numerical values which form a finite, or countably infinite, set of numbers
Continuous, quantitative data
Data obtained by observing numerical values which form some interval of numbers
possible methods of graphical deception include:
- stretching the vertical axis or shrinking the horizontal axis - only absolute changes in value, rather than percentages changes, are reported - a graph without a scale on one axis - a caption that influences the impression of the viewer
An experiment investigated the effect of length and repetition of TV ads on students choosing to eat at Del Taco. All 60 students watched a 40-minute television program that included ads for Del Taco. Some students saw a 30-second commercial; others a 90-second commercial. The same commercial was shown either 1, 3, or 5 times during the program. After the viewing, each student was asked to rate their craving for Del Taco on a scale of 0 to 10. What are the subjects of this experiment?
60 students
Archaeologists plan to examine a sample of 5-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this?
A stratified random sample
A survey records many variables of interest to the researchers conducting the survey. Below are some of the variables from a survey conducted by the U.S. Postal Service. Which of the variables is categorical? A. County of residence. B. Age of respondent. C. Number of people, both adults and children, living in the household. D. Total household income, before taxes, in 1993. E. None of the above.
A. County of residence.
Which of the following is not a characteristic of graphical excellence? A. There is no distortion of what the data reveal B. The graph presents small data sets concisely and coherently while large data sets are easily presented in tabular form C. The ideas and concepts the statistician wants to deliver are clearly understood by the viewer of the graph D. The graph encourages the viewer to compare two or more variables to depict relationships between the variables or to explain how and why the observed results occurred E. The graph induces the viewer to address substance of the data and not the form of the graph
B. The graph presents small data sets concisely and coherently while large data sets are easily presented in tabular form
A news release for a diet product company reports: There's good news for the 65 million Americans currently on a diet. Its study showed that people who lose weight can keep it off. The sample was 20 graduates of the company's program who endorse it in commercials. The results of the sample are probably A. unbiased, but they could be more accurate. A larger sample size should be used. B. biased, overstating the effectiveness of the diet. C. biased, understating the effectiveness of the diet. D. None of the above.
B. biased, overstating the effectiveness of the diet.
In sampling, why is obtaining a representative sample important?
Because we are using the sample to draw conclusions about the entire population
You are less likely to be misled by a graph if you: A. Focus your attention on the numerical values that the graph represents B. Avoid being influenced by the caption of the graph C. Both A and B D. Neglect the scale used on the axes E. Both B and D
C. Both A and B
Relative frequency=
Class frequency/sum of all frequencies Example: Your team has won 9 games from a total of 12 games played: the Frequency of winning is 9. the Relative Frequency of winning is 9/12 X 100 = 75%
A description of different houses on the market includes the following three variables. Which of the variables is quantitative? A. The school district. B. The exterior paint colors. C. The street number. D. The monthly electric bill. E. None of the above.
D. The monthly electric bill.
A poll is sent out to 160 students at a high school. Only 23% bother to fill them out and return them. This an example of A. an insufficient sample size B. the placebo effect C. sampling variability D. participation bias E. sampling bias
D. participation bias
A sample of households in a community is selected at random from the telephone directory. In this community, 7% of households have no telephone, 13% have only cell phones, and another 29% have unlisted telephone numbers. The sample will certainly suffer from
Undercoverage
A doctor gives half of his/her patients in a study a treatment and the other half a placebo, but the patients do not know which they received.
a controlled experiment
A nurse gives a group of patients either the drug being studied or a placebo; however neither the nurse nor the patient knows which they are receiving. Only the person who prepared the doses knows
a double blind experiment
Can pleasant aromas help a student learn better? Two researchers believed that the presence of a floral scent could improve a person's learning ability in certain situations. They had twenty-two people work through a pencil and paper maze six times, three times while wearing a floral-scented mask and three times while wearing an unscented mask. The three trials for each mask closely followed one another. Testers measured the length of time it took the subjects to complete each of the six trials. They reported that, on average, the subjects wearing the floral-scented mask completed the maze more quickly than those wearing the unscented mask, though the difference was not statistically significant. This study is
an experiment, but not a double-blind experiment.
A new study examines the effects of regular exercise on child obesity by taking a survey of 500 children on their weight and exercise habits
an observational study
The Nurses' Health Study has interviewed a sample of more than 100,000 female registered nurses every two years since 1976. The study finds that " light-to-moderate drinkers had a significantly lower risk of death" than either nondrinkers or heavy drinkers. The Nursers' Health Study is
an observational study
A study of the effects of running on personality involved 231 male runners who each ran about 20 miles a week. The runners were given the Cattell Sixteen Personality Factors Questionnaire, a 187-item multiple-choice test often used by psychologists. A news report (The New York Times, Feb. 15, 1988) stated, The researchers found statistically significant personality differences between the runners and the 30-year-old male population as a whole. A headline on the article said, Research has shown that running can alter one's moods. This study was
an observational study, but not an experiment.
Data:
are the raw materials of statistics
Qualitative data can be graphically represented by using a(n):
bar graph
Fifteen percent of the students in a school of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) which can be used to present these data is (are)
both a bar graph and a pie chart
Another name for population data is
census data
A medical study, in which a treatment group is compared to a control group, is carried out to reduce the effect of
confounding factors
The distance traveled by a city bus each day
continuous
- The number of customers waiting in line at the grocery store - The number of errors found on a student's research paper - The number of students applying to graduate schools
discrete
A table, graph, or formula that provides the values of the observations and how often they occur is the
distribution of a data set
Another name for population distribution is
distribution of a variable
Cartons on milk are opened, and the volumes of the contents are measured.
experiment
Studying how patients respond when given a placebo.
experiment
Individual observations within each class may be found in a frequency distribution
false
The class interval in a frequency distribution is the number of data values that fall within each class
false
the class interval in frequency distribution is the number of data values that fall within each class
false
if several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the:
fewest classes
The number of observations that fall in a class
frequency
Which of the following must be avoided in designing a questionnaire?
leading questions
Qualitative data:
may be either numeric or nonnumeric
Which of the following does not characterize stratified random sampling?
nonrandom sampling is used
A new antibiotic is tested in effectiveness by recording how the drug works on patients that already take the drug.
observation
The sum of the relative frequencies for all classes will always equal:
one
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. The boldface number is a
parameter
A choral conductor has 1726 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1726, so she instead asks 658 singers in front and finds 25 who are professionals.
parameter- percentage of entire singers who are professional sample- singers who were asked type of bias- Convenience Sampling statistic- 25/658
The relative frequency of a class multiplied by 100
percentage
Data is collected from a:
population
The data set obtained by observing the values of a variable for an entire population is
population data
The distribution of population data is the
population distribution
A researcher is gathering data from four geographical areas designated: South=1; North=2; East=3; West=4. The designated geographical regions represent:
qualitative data
In a questionnaire, respondents are asked to mark their gender as male or female. Gender is an example of a:
qualitative variable
A marketing class designs two videos advertising an expensive Mercedes sports car. They test the videos by asking fellow students to view both (in random order) and say which makes them more likely to buy the car. Mercedes should be reluctant to agree that the video favored in this study will sell more cars because
results from students may not generalize to the older and richer customers who might buy a Mercedes.
A data set obtained by observing the values of a variable for a sample of the population is
sample data
The distribution of sample data is a
sample distribution
The difference between a sample mean and the population mean is called:
sampling error
Standard deviation
square root of variance
The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sample of 60000 households; 4.9% of the people interviewed were unemployed. The boldface number is a
statistic
When the population is divided into mutually exclusive sets, and then a simple random sample is drawn from each set, this is called:
stratified random sampling
An opinion poll contacts 1273 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?" In all, 571 of the 1273 say, " The Democrats." The sample in this setting is
the 1273 people interviewed
The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that
the average burnout time of a large number of bulbs has a distribution that is close to Normal
the sum of the frequencies will always equal
the number of elements in a data set
A cumulative frequency distribution lists the number of observations that are within or below each of the classes
true
A relative frequency distribution describes the proportion of data values that fall within each category
true
a relative frequency distribution describes the proportion of data values that fall within each category
true
a stem-and-leaf display reveals far more information relative to individual values than does the histogram
true
in the term "frequency distribution" frequency refers to the number of data values falling within each class
true
Can changing diet reduce high blood pressure? Vegetarian diets and low-salt diets are both promising. Men with high blood pressure are assigned at random to one of four diets: (1) normal diet with unrestricted salt; (2) vegetarian with unrestricted salt; (3) normal with restricted salt; and (4) vegetarian with restricted salt. This experiment has
two factors, normal/vegetarian diet and unrestricted/restricted salt
