Deck 1: Introduction to Statistics

Question 1

Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.

-An employee at the local ice cream parlor asks three customers if they like chocolate ice cream.

Answer 1

Sample: the 3 selected customers; population: all customers; not representative

Question 2

An advertisement for a heating pad says that it can reduce back pain by 200%. What is wrong with this statement?

Answer 2

If a person's back pain was reduced by 100%, it would be completely eliminated, so it is not possible for a person's back pain to be reduced by more than 100%.

Question 3

Define the terms "stratified sampling", "systematic sampling", "cluster sampling", and "convenience sampling". Give examples for each.

Answer 3

Stratified sampling subdivides the population into at least two different subpopulations and then draws a sample from each stratum. Systematic sampling selects a beginning point and then selects every kth element in the population. In cluster sampling, the population is divided into sections, then sections are randomly selected, and then all members of the randomly selected sections are surveyed.
Convenience sampling uses readily available results. Examples will vary.

Question 4

A teacher at a school obtains a sample of students by selecting a random sample of 20 students from each grade. What kind of sampling is being used here? Will the resulting sample be a simple random sample of the population of students at the school? Explain your thinking.

Question 5

Use critical thinking to determine whether the sampling method appears to be sound or is flawed.

-A questionnaire is sent to 10,000 persons. 5,000 responded to the questionnaire. 3,000 of the respondents say that they "love chocolate ice cream". We conclude that 60% of people love chocolate ice cream. What is wrong with this survey?

Question 6

A bus company claims that in the past year it has reduced the number of late departures of buses by 100%. What is wrong with this statement?

Question 7

Define observational study and experiment. Define the terms "treatment group" and "placebo group" as part of your answer.

Question 8

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or

-Last year, the average math SAT score for students at one school was 475. The headmaster introduced new teaching methods hoping to improve scores. This year, the mean math SAT score for a sample of students was 481. Is there statistically significant evidence that the new teaching method is effective? If the teaching method had no effect, there would be roughly a 3 in 10 chance of seeing such an increase. Does the result have statistical significance? Why or why not? Does the result have practical significance?

Question 9

A researcher conducts an experiment to determine whether acupuncture can help people to recover from back injuries. Participants are randomly assigned to a treatment group or a control group. Over a period of three weeks, those assigned to the treatment group receive acupuncture treatments. At the end of the three weeks, the improvement reported by those in the treatment group is compared with the improvement reported by those in the control group. In this experiment there is no blinding. What does this mean and why could this cause a problem?

Question 10

Define random sample. Explain why this is important in design of experiments.

Question 11

Define the terms population, sample, parameter and statistic. How does a census compare to a sample?

Question 12

Distinguish between categorical and quantitative data. Give an example for each.

Question 13

Explain what is meant by the term "confounding" and give an example of an experiment in which confounding is likely to be a problem.

Question 14

List five different abuses of statistics and give examples for each.

Question 15

A student surveyed a simple random sample of students at her college. Is this sample likely to be representative of all students at her college? Of all adults in the United States?
Explain.

Question 16

Use critical thinking to determine whether the sampling method appears to be sound or is flawed.

-You plan to make a survey of 200 people. The plan is to talk to every 10th person coming out of the school library. Is there a problem with your plan?

Question 17

Use critical thinking to determine whether the sampling method appears to be sound or is flawed.

-A researcher published this survey result: "74% of people would be willing to spend 10 percent more for energy from a non-polluting source". The survey question was announced on a national radio show and 1,200 listeners responded by calling in. What is wrong with this survey?

Question 18

An airline company advertises that 100% of their flights are on time after checking 5 randomly selected flights and finding that these 5 were on time. What is wrong with their claim?

Question 19

Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.

-100,000 randomly selected adults were asked whether they drink at least 48 oz of water each day and only 45% said yes.

Question 20

An article stated that last year 807 people taking a certain medication suffered from serious side effects while this year, after the medication had been modified, only 391 suffered serious side effects. What information is missing? Why would it be important to include this information?

Question 21

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results.

-A researcher investigated whether following a vegetarian diet could help to reduce blood pressure. For a sample of 85 people who followed a vegetarian diet for 4 months, the mean systolic blood pressure was 124 mmHg and for a sample of 75 people who followed a nonvegetarian diet for 4 months, the mean systolic blood pressure was 138 mmHg.
Methods of statistics show that if a vegetarian diet had no effect on blood pressure, there would be less than 1 chance in a 100 of getting these results. Does the result have statistical significance? Why or why not? Does the result have practical significance?

Question 22

Define continuous and discrete data and give an example of each.

Question 23

Define sampling error and nonsampling error. Give examples of nonsampling error.

Question 24

Explain the difference between stratified and cluster sampling.

Question 25

Why do you think that cluster sampling is frequently used in practice.

Question 26

Would an observational study or an experiment be more appropriate to investigate the effects on humans of a substance known to be toxic? Explain.

Question 27

Use critical thinking to determine whether the sampling method appears to be sound or is flawed.

-"7 out of 10 dentists recommend Brand X toothpaste". This finding is based on the results of a survey of 10 randomly selected dentists. What is wrong with this survey?

Question 28

A market researcher obtains a sample of 50 people by standing outside a store and asking every 20th person who enters the store to fill out a survey until she has 50 people. What sampling method is being used here? Will the resulting sample be a random sample? Will it be a simple random sample? Explain your thinking.

Question 29

A group of men aged 50-59 followed a strict exercise regime for one year. The mean reduction in systolic blood pressure at the end of the year was 2.7 mmHg. Methods of statistics were used to determine that if the exercise regime had no effect on blood pressure, the likelihood of seeing this reduction in blood pressure by chance would be less than 1 in 100. Do the results have statistical significance? Do they have practical significance? Explain.

Question 30

Use critical thinking to develop an alternative conclusion.

-In a study of headache patients, every one of the study subjects with a headache was found to be improved after taking a week off of work. Conclusion: Taking time off work cures headaches.

Question 31

Does systematic sampling result in a random sample? Why or why not?

Question 32

A manufacturer of laptop computers claims that only 1% of their computers are defective. In a sample of 600 computers, it was found that 3% were defective. If the proportion of defectives were really only 1%, there would be less than 1 chance in 1000 of getting such a large proportion of defective laptops in the sample. Is there statistically significant evidence against the manufacturer's claim? Why or why not?

Question 33

Use critical thinking to develop an alternative conclusion.

-A study of achievement scores by sixth-grade students on a standardized math test showed the three top scorers were all gifted piano players. Conclusion: Playing the piano leads to mathematical achievement.

Question 34

Use critical thinking to determine whether the sampling method appears to be sound or is flawed.

-"38% of adults in the United States regularly visit a doctor". This conclusion was reached by a college student after she had questioned 520 randomly selected members of her college. What is wrong with her survey?

Question 35

At a school there are two different math classes of the same age. The two classes have different teachers. The school principal is interested in gauging the effectiveness of two different teaching methods and asks each teacher to try one of the methods. At the end of the semester both classes are given the same test and the results are compared. In this experiment, what is the variable of interest? Give some examples of variables which could be confounding variables.

Question 36

A researcher wants to obtain a sample of 100 school teachers from the 800 school teachers in a school district. Describe procedures for obtaining a sample of each type: random, systematic, convenience, stratified, cluster.

Question 37

Define and give examples for nominal, ordinal, interval, and ratio levels of measurement. Describe the type of statistics which might be reported for each.

Question 38

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results.

-Charlie's teacher claims that he does not study and just guesses on exams. On an exam with 201 true-false questions, Charlie answered 53.7% of the questions correctly.
Calculations using these results show that if he were really just guessing, there would be roughly 1 chance in 7 that he would do this well. Is there statistically significant evidence against the teacher's claim that Charlie is just guessing? Why or why not?

Question 39

A lawyer surveyed a simple random sample of his colleagues and asked them whether they were left-handed or right-handed. Is this convenience sample likely to provide results typical of all adults in the United States? Do convenience samples in general provide good results?

Question 40

A researcher obtains a sample of high school teachers in his school district by randomly selecting 10 high schools and interviewing all the teachers at each of these 10 schools.
What kind of sampling is being used here? Will the resulting sample be a simple random sample of the population of teachers in the school district? Explain your thinking.

Question 41

which of these types of sampling is used:

-A researcher interviews 19 work colleagues who work in his building.

A) Systematic
B) Cluster
C) Random
D) Stratified
E) Convenience

Question 42

Describe a double blind experiment and explain why blinding is used. Define the term "placebo effect" as part of the answer.

Question 43

Determine whether the given description corresponds to

-A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.

A) Experiment
B) Observational study

Question 44

Determine which of the four levels of measurement

-Ages of survey respondents.

A) Ratio
B) Nominal
C) Interval
D) Ordinal

Question 45

Jon consulted with an accountant to prepare his tax return. He recommended the accountant to his friend saying that this year the amount he paid in taxes was 150% less than last year. What is wrong with this statement?

Question 46

Determine whether the given description corresponds to an

-A sample of fish is taken from a lake to measure the effect of pollution from a nearby factory on the fish.

A) Experiment
B) Observational study

Question 47

In a clinical trial for a new headache medication, participants are randomly assigned to a treatment group or a placebo group. They do not know whether they are receiving the medication or a placebo. However the doctors administering the medication and evaluating the results do know which participants are receiving the medication. This experiment is blind but not double blind. Explain what this means and why the absence of double blinding could cause a problem.

Question 48

Determine whether the given description corresponds to an

-A marketing firm does a survey to find out how many people use a product. Of the one hundred people contacted, fifteen said they use the product.

A) Experiment
B) Observational study

Question 49

Determine whether the given value is from

-The number of limbs on a 2-year-old oak tree is 21.

A) Discrete
B) Continuous

Question 50

which of these types of sampling is used:

-A market researcher selects 500 people from each of 10 cities.

A) Cluster
B) Stratified
C) Systematic
D) Random
E) Convenience

Question 51

Determine whether the given

-A sample of 120 employees of a company is selected, and the average age is found to be 37 years.

A) Parameter
B) Statistic

Question 52

Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or make subjective judgments about the results.

-In a random sample of 160 women, 78% favored stricter gun control laws. In a random sample of 220 men, 61% favored stricter gun control laws. Is there statistically significant evidence that a larger proportion of women than men favor stricter gun control laws?

Question 53

Determine which of the four levels of measurement

-The subjects in which college students major.

A) Ratio
B) Ordinal
C) Nominal
D) Interval

Question 54

Use critical thinking to develop an alternative conclusion.

-A study shows that adults who work at their desk all day weigh more than those who do not. Conclusion: Desk jobs cause people to gain weight.

Question 55

which of these types of sampling is used:

-To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.

A) Convenience
B) Random
C) Systematic
D) Stratified
E) Cluster

Question 56

Does stratified sampling result in a simple random sample? Why or why not?

Question 57

The type of observational study

-Researchers collect data by interviewing athletes who have won olympic gold medals from 1992 to 2008.

A) Prospective
B) Retrospective
C) Cross-sectional
D) None of these

Question 58

A teacher was interested in knowing how much tax people pay in the United States. She selected a simple random sample of her friends and asked them about their taxes. Is this sample likely to be representative of all adults in the United States?

Question 59

Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.

-In a poll of 50,000 randomly selected college students, 74% answered "yes" when asked "Do you have a television in your dorm room?".

Question 60

A hip hop radio show broadcast in the city of Puddelton asked people to call in and express their opinions on the new mayor. Are the results likely to be representative of all adults in Puddelton? Of all listeners to the hip hop show? Why or why not?

Question 61

Determine whether the given value is from

-The temperature of a cup of coffee is 67.3°F.

A) Discrete
B) Continuous

Question 62

Determine whether the given description corresponds to

-A T.V. show's executives raised the fee for commercials following a report that the show received a "No. 1" rating in a survey of viewers.

A) Observational study
B) Experiment

Question 63

Determine whether the given value is

-The weight of Bill's pack as he sets off on a backpacking trip is 48.3 lb.

A) Continuous
B) Discrete

Question 64

An electronics store receives a shipment of eight boxes of calculators. Each box contains ten calculators. A quality control inspector chooses a box by putting eight identical slips of paper numbered 1 to 8 into a hat, mixing thoroughly and then picking a slip at random. He then chooses a calculator at random from the box selected using a similar method with ten slips of paper in a hat.
He repeats the process until he obtains a sample of 5 calculators for quality control testing. Does this sampling plan result in a random sample? Simple random sample? Explain.

A) No; yes. The sample is not random because not all calculators have the same chance of being selected. It is a simple random sample because all samples of 5 calculators have the same chance of being selected.

B) Yes; no. The sample is random because all calculators have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing 5 calculators from the same box.

C) Yes; yes. The sample is random because all calculators have the same chance of being selected. It is a simple random sample because all samples of 5 calculators have the same chance of being selected.

D) No; no. The sample is not random because not all calculators have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing 5 calculators from the same box.

Question 65

which of these types of sampling is used

-An education researcher randomly selects 48 middle schools and interviews all the teachers at each school.

A) Random
B) Cluster
C) Stratified
D) Convenience
E) Systematic

Question 66

Determine whether the given value is

-After inspecting all of 55,000 kg of meat stored at the Wurst Sausage Company, it was found that 45,000 kg of the meat was spoiled.

A) Parameter
B) Statistic

Question 67

On a test, if 40 questions are answered and 38 of them are correct, what is the percent of correct answers? Round to the nearest percent.

A) 105%
B) 5%
C) 0.95%
D) 95%

Question 68

Determine whether the given value is

-The height of 2-year-old maple tree is 28.3 ft.

A) Discrete
B) Continuous

Question 69

A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157 lb.

A) Parameter
B) Statistic

Question 70

Alex and Juana went on a 70-mile canoe trip with their class. On the first day they traveled 14 miles. What percent of the total distance did they canoe?

A) 500%
B) 0.2%
C) 5%
D) 20%

Question 71

A researcher obtains an alphabetical list of the 2560 students at a college. She uses a random number generator to obtain 50 numbers between 1 and 2560. She chooses the 50 students corresponding to those numbers. Does this sampling plan result in a random sample? Simple Random sample? Explain.

A) Yes; no. The sample is random because all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing the first 50 students on the list.

B) No; no. The sample is not random because not all students have the same chance of being selected. It is not a simple random sample because some samples are not possible, such as a sample containing the the first 50 students on the list.

C) Yes; yes. The sample is random because all students have the same chance of being selected. It is a simple random sample because all samples of 50 students have the same chance of being selected.

D) No; yes. The sample is not random because not all students have the same chance of being selected. It is a simple random sample because all samples of 50 students have the same chance of being selected.

Question 72

Determine whether the given description corresponds to

-A doctor performs several diagnostic tests to determine the reason for a patient's illness.

A) Experiment
B) Observational study

Question 73

Determine whether the given value is

-After taking the first exam, 15 of the students dropped the class.

A) Parameter
B) Statistic

Question 74

The number of freshmen entering college in a certain year is 621.

A) Discrete
B) Continuous

Question 75

A statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years.

A) Cross-sectional
B) Retrospective
C) Prospective
D) None of these

Question 76

Determine which of the four levels of measurement is most appropriate.

-The sample of spheres categorized from softest to hardest.

A) Ratio
B) Ordinal
C) Nominal
D) Interval

Question 77

Determine which of the four levels of measurement is most appropriate.

-Temperatures of the ocean at various depths.

A) Interval
B) Ordinal
C) Nominal
D) Ratio

Question 78

A researcher plans to obtain data by following those in cancer remission since January of 2005.

A) Retrospective
B) Prospective
C) Cross-sectional
D) None of these

Question 79

Determine whether the given value is

-The number of stories in a Manhattan building is 22.

A) Discrete
B) Continuous

Question 80

Determine which of the four levels of measurement is most appropriate.

-The temperatures of eight different plastic spheres.

A) Nominal
B) Interval
C) Ratio
D) Ordinal