# Intro. To Statistics MCCC Ch. 1

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What is a voluntary response sample?
A sample in which the subjects themselves decide whether to be included in the study.
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Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and dairy products in ourโ diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.
There does appear a potential to create bias. There is an incentive to produce results that are in line with the organization's creed and that of its funders.
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Determine whether the source given below has the potential to create a bias in a statistical study. Washington University obtained word counts from the most popular novels of the past five years.
There does not appear a potential to create a bias. The organization would not gain from putting a spin on the results
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Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 628 subjects, each was asked how often he or she watched TV. The survey subjects were internet users who responded to a question that was posted on a news website.
It is flawed because it is a voluntary response sample.
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Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 611 human resource professionals, each was asked about the importance of the education of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
It appears to be sound because the data are not biased in any way.
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Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 5 subjects lost an average of 45 Ibs. It is found that there is about a 29% chance of getting such results with a diet that has no effect. Does the weight loss program have statistical significance? Does the weight loss program have practical significance?
No, the program is not statistically significant because the results are likely to occur by chance. Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.
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In a study of a weight loss program, 45 subjects lost a mean of 3.1 Ibs after 12 months. Methods of statistics can be used to show that if this diet had no effect, the likelihood of getting these results is roughly 6 chances in 1000. Does the weight loss program have statistical significance? Does the weight loss program have practical significance?
Yes, because the results are unlikely to occur by chance. No, someone starting a weight loss program would likely want to lose considerably more than 3.1 Ib.
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Several studies showed that after eating 4 servings of dairy a day, subjects had lowered risk of osteoporosis. A dairy farmer's organization financed this research. What is wrong with this study?
Self-interest study
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Based on a study of car accidents in winter of men and women who live in different parts of the country, a researcher concludes that living in the north causes people to drive badly. Do you agree with this conclusion?
No. There may be a relationship between car accidents and geographical location, but that does not mean that one causes the other.
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A polling company reported that 59% of 1013 surveyed adults said that secondhand smoke is "quite annoying." a. What is the exact value that is 59% of 1013? b. Could the result from part (a) be the actual number of adults who said that secondhand smoke is "quite annoying"? Why or why not? c. What could be the actual number of adults who said that second hand smoke is "quite annoying"? d. Among the 1013 respondents, 301 said that secondhand smoke is "not at all annoying." What percentage of respondents said that secondhand smoke is "not at all annoying"?
a. 597.67 b. No, the result from part (a) could not be the actual number of adults who said that secondhand smoke is "quite annoying" because a count of people must result in a whole number. c. 598 d. 29.71%
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A polling company reported that 14% of 2302 surveyed adults said that they play football. a. What is the exact value that 14% of 2302? b. Could the result from part (a) be the actual number of adults who said that they play football? Why or why not? c. What could be the actual number of adults who said that they play football? d. Among the 2303 respondents, 497 said that they only play hockey. What percentage of respondents said that they only play hockey?
a. 322.28 b. No, the result from part (a) could not be the actual number of adults who said that they play football because a count of people must result in a whole number. c. 322 d. 21.59%
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An ad for airbags claimed that proper usage of airbags reduces the chance of fatality in a car crash by 250 percent. What is wrong with this statement?
If airbags eliminated all fatalities, it would result in a 100% reduction, so it is not possible to reduce fatalities by more than 100%.
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A report about the decline of Western investment in third world countries included this: "After years of daily flights, several European airlines halted passenger service. Foreign investment fell 400 percent during the 1990s. What is wrong with this statement?
If foreign investment fell by 100% it would be totally eliminated, so it is not possible for it to fall by more than 100%.
question
A researcher was once criticized for falsifying data. Among his data were figures obtained from 4 groups of mice, with 20 individual mice in each group. These values were given for the percentage of successes in each group: 53%, 58%, 63%, 46%. What's wrong with those values?
All percentages of success should be multiples of 5. The given percentages cannot be correct.
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Which of the following is typically the least important factor to consider when conducting a statistical analysis of data? a. Source of the data b. Sampling Method c. Formula Calculation d. Context of the data
c. Formula Calculation
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Which of the following is NOT a voluntary response sample? a. A radio station asks for call-in responses to a question concerning city recycling. b. A survey is taken at a mall by asking passersby if they will fill out the survey. c. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office visit. d. Quiz scores from a college level statistics course are analyzed to determine student progress.
d.
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What does it mean for the findings of a statistical analysis of data to be statistically significant?
the likelihood of getting these results by chance is very small
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If we are collecting sample data for a study, the -- that we choose can greatly influence the validity of our conclusions. For example, we can use sound statistical methods to analyze data in voluntary response samples, but the results are not necessarily valid.
sampling method
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Which of the following would be considered practically significant? a. 1 out of 50 people were not smoking 12 months after completing a non-smoking program. b. An average of 1.2 pounds was lost over a 12 month period using a new diet program. c. 8 out of 14 births resulted in male children. d. In a very large study, it was found that Treatment I resulted in 93% success while Treatment II resulted in 75% success.
d.
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What is the goal of learning statistics?
To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed.
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Which of the following is NOT a misuse of statistics? a. Concluding that a variable causes another variable because they have some correlation b. Making conclusions about a population based on a voluntary response sample c. Utilizing valid statistical methods and correct sampling techniques d. misleading graphs
c.
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Intentionally worded to elicit a desired response
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Which of the following would NOT cast doubt of the usefulness of sample data? a. Order of questions in a survey b. Nonresponse c. Missing data d. An effective sampling method
d.
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What is a self-interest study?
A survey in which the sponsor can enjoy monetary or other gains from the results
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How do a parameter and a statistic differ?
A parameter is a numerical measurement of a population; a statistic is a numerical measurement of a sample.
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Determine whether the given value is a statistic or a parameter. A survey found that 89% of all respondents go to school.
The value is a statistic because it is a numerical measurement describing some characteristic of a sample.
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Determine whether the given value is a statistic or a parameter. In a study of all 3919 employees at a college, it is found that 45% own a computer.
Parameter because the value is a numerical measurement describing a characteristic of a population.
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Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on all 365 days of a given year, and the average (mean) value is 105.1 volts.
The given value is a parameter for the year because the data collected represent a population.
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A particular country has 50 total states. If the areas of 20 states are added and the sum is divided by 20, the result is 205,145 square kilometers. Determine whether the result is a statistic or a parameter.
The result is a statistic because it describes some characteristic of a sample.
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Determine whether the given value is from a discrete or continuous data set. When a car is randomly selected, it is found to have an engine with 8 cylinders.
It is from a discrete data set because the number of possible values is finite or countable.
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Determine whether the given value is from a discrete or continuous data set. When a car is randomly selected, it is found to have 4 doors.
A discrete data set because there are a finite number of possible values.
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Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 11.4 oz.
A continuous data set because there are infinitely many possible values and those values cannot be counted
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Determine whether the value is from a discrete or continuous data set. Number of pieces of lumber used to make a deck is 113
Discrete
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Years of elections: 1988, 1992, 2000, and 2004
Interval
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate Favorite types of music
nominal
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Companies that produced movies in 2007
The nominal level of measurement is most appropriate because the data cannot be ordered
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Companies that produced movies in 2007.
The nominal level of measurement is most appropriate because data cannot be arranged in an ordering scheme.
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Years in which a war was started
The interval level of measurement is most appropriate because the data can be ordered, differences can be found and are meaningful, and there is no natural starting zero point.
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Bushels of wheat
The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting zero point.
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Serial numbers on cans
The nominal level of measurements is most appropriate because the data cannot be ordered
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Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the responses of respondents are identified as 10 for a "yes," 20 for a "no," 30 for a "maybe," and 40 for anything else. The average (mean) is calculated for 681 respondents and the result is 22.3. The data are at the - level of measurement. What is wrong with the given calculation?
nominal Such data are not counts or measures of anything, so it makes no sense to compute their average (mean).
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Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a set of data, car rankings are represented as 1 for first, 2 for second, and 3 for third. The average (mean) of the 636 car rankings is 1.3. The data are at the - level of measurement. What is wrong with the given calculation?
ordinal Such data should not be used for calculations such as an average.
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Which of the following is NOT a level of measurement? a. nominal b. quantitative c. ordinal d. ratio
b.
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Which of the following is associated with a parameter? a. A numerical measurement describing some characteristic of a sample. b. Data that were obtained from a voluntary poll at the end of a service call. c. Data that were obtained from a sample. d. Data that were obtained from an entire population.
d.
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Which of the following consists of discrete data? a. hair color b. amount of rainfall c. tree height d. number of suitcases on a plane
d.
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Which of the following would be classified as categorical data? a. hair color b. number of suitcases on a plane c. amount of rainfall d. tree height
a.
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Which level of measurement consists of categories only where data cannot be arranged in an ordering scheme?
nominal
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What is the difference between a random sample and a simple random sample?
With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
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Determine whether the description corresponds to an observational study or an experiment. Research is conducted to determine if there is a relation between stomach cancer and alcohol consumption. Does the description correspond to an observational study or an experiment?
observational study
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Determine whether the given description corresponds to an observational study or an experiment. In a study of 356 women with a particular disease, the subjects were injected with vitamins to determine if the vitamins have an effect on the disease. Does the given description correspond to an observational study or an experiment?
The given description corresponds to an experiment.
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Determine whether the description below corresponds to an observational study or an experiment. In a survey sponsored by a company, 10,979 people were asked what contributes most to their sadness, and 72% of the respondents said that it was their health. Is the study described above and observational study or an experiment?
The study is an observational study because the survey subjects were not given any treatment.
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Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman is selected by a marketing company to participate in a paid focus group. The company says that the woman was selected because every 7500th person in the phone number listings was being selected. Which type of sampling did the marketing company use?
systematic sampling
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Identify the type of sampling (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 1208 adults were called after their telephone numbers were randomly generated by a computer, and 32% were able to correctly identify the president. Which type of sampling did the research center use?
random sampling
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Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. An internet site asks its members to call in their opinion regarding their web searching habits. Which type of sampling is used?
Convenience
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Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at Ford selects every 18th truck that comes off the assembly line starting with the eighth until she obtains a sample of 60 trucks. Which type of sampling is used?
systematic
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Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman experienced a tax audit. The tax department claimed that the woman was audited because she was randomly selected from all the taxpayers. Which type of sampling did the tax department use?
random sampling
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Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their check-in service, American Airlines randomly selects 50 flights during a certain week and surveys all passengers on the flights. Which type of sampling is used?
cluster
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Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 441th social security number and surveys the corresponding person. Which type of sampling did the researcher use?
systematic sampling
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Determine whether the sample described below is a simple random sample. A quality control engineer selects every 11,000th can opener that is produced. Does this sampling plan result in a simple random sample?
The sample is not a simple random sample because every sample of the same size does not have the same chance of being selected.
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Determine whether the sample described below is a simple random sample. In order to test for a difference in the way that parents and non-parents purchase cars, a research institution polls exactly 862 adult parents and 862 adult non-parents randomly selected from adults in the United States. Does this sampling plan result in a simple random sample?
The sample is not a simple random sample because every sample of size 1724 does not have the same chance of being selected.
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Determine whether the sample described below is a simple random sample. In the last year, 150,170 adults paid taxes in a county. A researcher plans to conduct a survey of 900 of those taxpayers. After obtaining a list of those who paid taxes, he numbers the list from 1 to 150,170, and then he uses a computer to randomly generate 900 numbers between 1 and 150,170. His sample consists of the taxpayers corresponding to the selected numbers. Does this sampling plan result in a simple random sample?
The sample is a simple random sample because every sample of size 900 has the same chance of being selected.
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Determine whether the same described below is a simple random sample. According to a survey company, names of potential respondents are selected from a variety of different sources. Names from the list are randomly selected in a way that is equivalent to writing the names on slips of paper, mixing them in a bowl, and selecting the required number of potential respondents. Does this sampling plan result in a simple random sample?
The sample is a simple random sample because every sample of the same size has the same chance of being selected.
question
A handler loads one item every 15 minutes, so 160 items are completed in her first week of work. Her manager checks her work by randomly selecting a day of the week, then reviewing all the items she completed that day. Does this a sampling plan result in a random sample? Simple random sample? Does this sampling plan result in a random sample? Does this sampling plan result in a simple random sample?
Yes, because each item has an equal chance of being selected. No, because all possible groups of n items do not have an equal chance of being selected.
question
Identify the type of observational study. A researcher plans to obtain data by interviewing offspring of victims who perished in a tornado. He will interview them, and people unrelated to the victims, over the next 10 years to see how closeness to a traumatic event might affect recovery time. Choose the correct type of observational study below. a. cross-sectional b. prospective c. retrospective
b.
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Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 5000 households, and the data collected today will be used to determine the proportion of households tune to a particular news program. Which type of observational study is described in the problem statement?
a cross-sectional study
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Which sampling method divides the population up into sections, randomly selects some of these sections, then chooses all the members from the selected sections to study?
cluster
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Which sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each subdivision?