BAI 210 exam 1
Which of these are possible dangers of nonresponse? Select all that apply.
-Those who feel strongly about the subject are more likely to respond. -Those who do not feel strongly about the subject are less likely to respond.
Data on the length, in seconds, of a sample of 50 songs by The Beatles are presented in the accompanying data table. Complete parts (a) through (d) below.
Both the frequency histogram and the dotplot show most of the values being clustered between 100 and 200 seconds. The dotplot allows for showing the relative positions of the data more precisely.
descriptive statistics
consists of organizing and summarizing information collected
What is the acronym used for simple random sampling without replacement?
SRR
The members of a population have been numbered 1-50. A sample of size 20 is to be taken from the population, using cluster sampling. The clusters are of equal size 10, where cluster #1 consists of the members of the population numbered 1-10, cluster #2 consists of the members of the population numbered 11-20, and so forth. a. What are the clusters taken from the population?
1-10, 11-20, 21-30, 31-40, 41-50
In a designed experiment, there is one factor with four levels. How many treatments are there?
4
According to Chebyshev's rule, at least ... of the observations in any data set lie within 2.5 standard deviations to either side of the mean.
84%
According to Chebyshev's rule, at least enter your response here% of the observations in any data set lie within four standard deviations to either side of the mean.
93.75%
What is a truncated graph?
A graph where part of the one of the axes has been cut off or truncated
Percentage vs relative frequency
A relative frequency is the same as a percentage expressed as a decimal.
One characteristic measured about high schools is the percent free lunch, which is the percentage of the student body that is eligible for free and reduced-price lunches. The top 100 schools, grouped according to their percent free lunch, is as shown in the accompanying table. Complete parts (a) and (b) below.
Choose 55/100 of the sample from 0-under 10, choose 16/100 of the sample from 10-under 20, choose 6/100 of the sample from 20-under 30, choose 6/100 of the sample from 30-under 40, and choose 17/100 of the sample from 40 or over. Multiply each fraction by 25 to get the sample size for each group, adjusting the values to integers if needed. Then use a random number generator to select the chosen number of schools from each group.
What are the two major types of statistics? Describe them in detail.
Descriptive statistics consists of organizing and summarizing informationcollected, while inferential statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.
What are the two major types of statistics?
Descriptive and Inferential
b. Choose the correct answer below.
In a designed experiment, researchers impose treatments and controls and then observe characteristics and take measurements.
a. Choose the correct answer below.
In an observational study, researchers simply observe characteristics and take measurements, as in a sample survey.
Complete the following statement: A descriptive measure is resistant if...
It is not sensitive to the influence of a few extreme observations.
Give a legitimate motive for truncating the axis of a graph. Choose the correct answer below.
It may allow relevant information to be conveyed more easily.
Presented below is a "data scenario." Decide which type of grouping (single-value, limit, or cutpoint) is probably the best. The times, rounded to the nearest minute, of athletes in a marathon
Limit grouping is probably the best because the data are whole numbers and there are a large number of distinct values.
Do the concepts of class limits, marks, cutpoints, and midpoints make sense for qualitative data? Explain your answer.
No. Class limits, marks, cutpoints, and midpoints make sense only for numerical data, because doing arithmetic for qualitative data is not meaningful.
Ordinal data is data about order or rank given on a scale such as 1, 2, 3, ... or A, B, C, ... Does the following variable yield ordinal data? Gender
No, because the data are not ordered in some way
Select the correct choice that completes the sentence below.
Observational studies can reveal only association, whereas designed experiments can help establish causation
If you have a legitimate motive for truncating the axis of a graph, how can you correctly obtain that objective without creating the possibility of misinterpretation?
Start the axis at 0 and include a special symbol, such as slashes, to indicate that part of the axis is missing.
Select the correct choices that complete the sentence below.
Systematic random sampling is easier to execute than simple random sampling and usually provides comparable results. The exception is the presence of some kind of cyclical pattern in the listing of the members of the population.
b. Which measure of variation is preferred when the median is used as a measure of center?
The interquartile range is preferred when the median is used as a measure of center.
a. Which measure of variation is preferred when the mean is used as a measure of center?
The standard deviation is preferred when the mean is used as a measure of center.
A board of governors publishes information on family net worth. In 2010, the mean net worth of families in a particular country was $456.1 thousand and the median net worth was $78.3 thousand. Which measure of center do you think is more appropriate? Explain your answer
The median because it is not strongly affected by the relatively few families with extremely high net worth.
b. Is the percentage provided a descriptive statistic or an inferential statistic? Explain your answer.
The percentage is a descriptive statistic, since it summarizes information about how much of the sample favors breaking up the megabanks.
A nationwide survey of 1000 adults found that 50% of respondents favored a plan to break up the 12 megabanks, which then controlled about 69% of the banking industry. Complete parts (a) and (b) below. a. Identify the population and sample for this study. Choose the correct answer below.
The population is all adults in the country. The sample is the 1000 adults surveyed.
Explain in detail the purpose of a measure of center.
The purpose of a measure of center is to indicate where the center or most typical value of a data set lies.
b. What does it measure?
The range of the middle 50% of the observations
Why is obtaining a representative sample important?
The sample must be representative in order to use inferential statistics to draw conclusions about the entire population.
What is a consequence of such low response rates?
The samples are not likely to be representative of their respective populations.
State whether the investigation in question is an observational study or a designed experiment. Justify your answer. In a paper in a medical journal, researchers reported the results of a study of methods for treating patients who had advanced heart failure due to ischemic or nonischemic cardiomyopathies. A total of 1370 patients were randomly assigned in a 1:1:2 ratio to receive optimal pharmacologic therapy alone or in combination with either a pacemaker or a pacemaker-defibrillator combination. The patients were then observed until they died or were hospitalized for any cause.
The study is a designed experiment because the researchers controlled the treatment of the subjects.
State whether the investigation in question is an observational study or a designed experiment. Justify your answer. In the article "One's Sex, Sleep, and Posttraumatic Stress Disorder", I. Kobayashi et al. study the relationship between one's sex, sleep patterns, and posttraumatic stress disorder (PTSD) after trauma exposure. The authors report that women have a higher lifetime prevalence of PTSD as well as a greater risk of developing PTSD following trauma exposure. Relationships between sleep and physical health have been documented in a number of studies, and the authors explore the possibility that disruptive sleep habits are common among people with PTSD and also a possible risk factor for the development of PTSD. A questionnaire of men and women with and without PTSD produced data on their sleep habits. Question content area bottom Part 1 Is the investigation an observational study or a designed experiment?
The study is observational because the researchers did not impose any conditions on the subjects before collecting the data.
Classify the study as either descriptive or inferential. Explain your answer. The table below shows data on average professional athletes' salaries for the years 2005 and 2011.
The study is descriptive, because the statistics are a summary of the average salaries of professional athletes in three sports.
Classify the study as either descriptive or inferential. Explain your answer. A company provides an online database that provides real estate information for homes that are for rent or sale in a certain country. It also presents statistics on recently sold homes. The following table gives various information on all homes sold in several different cities in the country for one month.
The study is descriptive, because the table is a summary of the data that was collected.
Classify the study as either descriptive or inferential. Explain your answer. Data from a sample of citizens of a certain country yielded the following estimates of average TV viewing time per month for all citizens 2 years old and older. The times are in hours and minutes; Q1 stands for first quarter.
The study is inferential, because the statistics are used to make an inference about the population.
Researchers in obesity wanted to compare the effectiveness of dieting with exercise against dieting without exercise. Seventy-three patients were randomly divided into two groups. Group 1, composed of 38 patients, was put on a program of dieting with exercise. Group 2, composed of 35 patients, dieted only. The results for the weight loss, in pounds, after 5 months are summarized in the following boxplots. The top boxplot is for Group 1 and the bottom boxplot is for Group 2. Use the boxplots to compare the weight losses for the two groups, paying special attention to center and variation.
The weight losses for the two groups are, on average, roughly the same. However, there is less variation in the weight losses of Group 1 than of Group 2.
Name and describe the three most important measures of center.
The mean, median, and mode are the most important measures of center. The mean of a data set is its arithmetic average. The median of a data set is the middle value in its ordered list. The mode of a data set is its most frequently occurring value.
c. Which stem-and-leaf diagram is more useful? Why?
The stem-and-leaf diagram with one line per stem is more useful, since the shape of the distribution is apparent in both diagrams but the diagram with two lines per stem has a large number of empty stems.
Slightly different methods are used for determining the "middle" of a class with limit grouping and cutpoint grouping. Identify the methods and the corresponding terminologies.
With limit grouping, the "middle" of a class is the average of the two class limits of the class; it is called the class mark. With cutpoint grouping, the "middle" of a class is the average of the two cutpoints of the class; it is called the class midpoint.
Which type of variable yields nonnumerical data?
qualitative
designed experiment
researchers impose treatments and controls and then observe characteristics and take measurements
observational study
researchers simply observe characteristics and take measurements, as in a sample survey. Can reveal only association, whereas designed experiments can help establish causation.
A sample distribution is the distribution of
sample data
frequency
the number of times a particular distinct value occurs
relative frequency
the ratio of the frequency of a value to the total number of observations
inferential statistics
uses methods that generalize results obtained from a sample to the population and measure the reliability of the results
Is an extreme observation necessarily an outlier? Explain your answer.
No, it is only a potential outlier. Further data analyses are necessary to determine if it is truly an outlier.
Discuss the relative advantages and disadvantages of stem-and-leaf diagrams versus frequency histograms.
Stem-and-leaf diagrams are easier to make and can contain more information than frequency histograms. However, they are not very useful for large data sets.
