ISDS Final Exam
empirical probability
involves conducting an experiment to observe the frequency with which an event occurs
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean
is closer to a normal distribution
For k> 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within
k standard deviations from the mean
When comparing two population means, their hypothesized difference
may assume any value
The ordinal scale of data measurement is
more sophisticated than the nominal scale.
The mode is defined as the
most frequent value in a data set.
Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?
A larger sample size reduces the margin of error.
What may be revealed from a scatterplot?
A linear relationship between two variables No relationship between two variables A curvilinear relationship between two variables all of the above
Which of the following meets the requirements of a simple random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.
Which of the following is an example of time series data? The sale prices of townhouses sold last year Results of market research testing consumer preferences for soda Quarterly housing starts collected over the last 60 years Starting salaries of recent business graduates at Penn State University
Quarterly housing starts collected over the last 60 years
What is the scale of measurement of the distance between any two locations?
Ratio scale
Which of the following is an example of cross-sectional data? GDP of the United States from 1990-2010 Results of market research testing consumer preferences for soda The daily price of DuPont stock during the first quarter Quarterly housing starts collected over the last 60 years
Results of market research testing consumer preferences for soda
When displaying quantitative data, what is an ogive used to plot?
Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class
In order to summarize qualitative data, a useful tool is a
Frequency Distribution
Which of the following is an example of quantitative data? The ZIP code of your home address Google's closing stock price today Your gender Your Social Security number
Google's closing stock price today
Which of the following is appropriate to conduct a hypothesis test for the difference between two population proportions under independent sampling.
Only if n1p⎯⎯1≥5,n1(1−p⎯⎯1)≥5,n1p¯1≥5,n1(1−p¯1)≥5, n2p⎯⎯2≥5n2p¯2≥5 , and n2(1−p⎯⎯2)≥5.
A respondent of a survey is asked whether the Philadelphia Flyers' performance in the last game was excellent, good, fair, or poor. The person indicates that the performance was "good." This is an example of
Ordinal Data
An undergraduate student's status (freshman, sophomore, junior, or senior) is an example of which scale of measurement?
Ordinal scale
When using the empirical rule, which of the following assumptions is made?
The data are approximately symmetric and bell-shaped.
Assume the sample space S = {win, loss}. Select the choice that fulfills the requirements of the definition of probability.
P({win}) = 0.7, P({loss}) = 0.3
The Study of statistics can best be described as
The language of data the art and science of getting information from data the study of collecting, organizing, analyzing, and interpreting data.
When using a polygon to graph quantitative data, what does each point represent?
The midpoint of a particular class and its associated frequency or relative frequency
For both qualitative and quantitative data, what is the difference between the relative frequency and the percent frequency?
The percent frequency equals the relative frequency multiplied by 100.
How do the tdf and z distributions differ?
The tdf distribution has broader tails (it is flatter around zero).
For a multinomial experiment, which of the following is not true?
The trials are dependent.
Which of the following capabilities does Analysis of Relative Location provide?
They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.
What is the purpose of calculating a confidence interval?
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.
is it possible for a data set to have no mode?
Yes, if there are no observations that occur more than once.
Which of the following is an example of qualitative data? The class average of last test The amount of time you spent for your homework Your last name today's high temperature
Your Last name
Which of the following is not a graphical technique to display quantitative data?
bar chart
Classical Probability
based on logical analysis
Population parameters are difficult to calculate due to
both cost prohibitions on data collection and the infeasibility of collecting data on the entire population.
Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?
np≥5 and n(1−p)≥5
A sample statistic is an estimate of
population parameter.
The choice of an appropriate test for comparing two population means depends on whether we deal with
qualitative or quantitative data independent or matched-pairs sampling the equality or lack of equality of population variances
In any production process, variations in the quality of the end product are inevitable. Assignable variation refers to
specific events or factors that can usually be identified and eliminated
Two or more random samples are considered independent if
the process that generates one sample is completely separate from the process that generates the other sample
In its standard form, Chebyshev's theorem provides a lower bound on
the proportion (or percentage) of observations lying within a certain interval
Bias can occur in sampling. Bias refers to
the tendency of a sample statistic to systematically over- or underestimate a population parameter
For a chi-square test of a contingency table, the degrees of freedom are calculated as (r−1)(c−1) where r and c are the number of rows and columns in the contingency table.
true
The chi-square goodness-of-fit test is a right-tailed test.
true, can never be left
The chi-square test of a contingency table is a test of independence for
two qualitative variables
When a characteristic of interest differs among various observations, then it can be termed a
variable.
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been
wider; smaller
Which five values are graphed on a box plot?
Min, Quartile 1, Median, Quartile 3, Max
Which of the following scales represents the least sophisticated level of measurement?
Nominal
The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is
1/(b - a) between a and b, and zero otherwise
Which scale of data measurement is appropriate for the names of companies listed on the Dow Jones Industrial Average?
Nominal scale
Which of the following meets the requirements of a stratified random sample?
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.
When interpreting the covariance between variables x and y, which of the following statements is the most accurate?
A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean.
Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value?
A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. The z value corresponding to x = μ is zero.
How does an ogive differ from a polygon?
An ogive is a graphical depiction of a cumulative frequency or cumulative relative frequency distribution, while a polygon is a graphical depiction of a frequency or relative frequency distribution.
Which of the following is true when using the empirical rule for a set of sample data?
Approximately 68% of all observations are in the interval x plus or minus s
Which of the following represents an empirical probability?
Based on past observation, a manager believes there is a three-in-five chance of retaining an employee for at least one year.
What is an advantage of the correlation coefficient over the covariance?
Both answers-that it falls between -1 and 1 and that it is a unit-free measure-are correct.
How do we find the median if the number of observations in a data set is odd?
By taking the middle value in the sorted data set
Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?
Independent sampling with quantitative data
A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x)
Is constant for all x between a and b, and 0 otherwise
Which of the following statements about the mean absolute deviation (MAD) is the most accurate?
It is measured in the same units as the original data.
How does the variance of the sample mean compare to the variance of the population?
It is smaller and therefore suggests that averages have less variation than individual observations.
John would like to conduct a survey in his neighborhood to get homeowners' opinion on Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample?
John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional amount of houses from each group.
The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary, by 20%. Which of the following is(are) expected to be affected by this raise?
Mean only
What is(are) the most widely used measure(s) of dispersion?
Variance and standard deviation
Chebyshev's theorem is applicable when the data are
any shape
The Fahrenheit scale for measuring temperature would be classified as a(n)
interval scale.
An analyst studies a data set of the year-end book value per share for all companies listed on the New York Stock Exchange. This data set is best described as
cross-sectional data
Your business statistics class had a test last week. The average score for the class is an example of
descriptive statistics
subjective probability
drawn on personal judgement
Horizontal bar charts are constructed by placing
each category on the vertical axis and the appropriate range of values on the horizontal axis
Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n)
estimate
In inferential statistics, we calculate the sample data to
estimate unknown population parameters. conduct tests about unknown population parameters.
For a multinomial experiment with k categories, the goodness-of-fit test statistic is assumed to follow a chi-square distribution with k degrees of freedom.
false
Which of the following variables is qualitative? Height gender weight temp
gender
Which of the following is not true concerning the attributes of z-scores?
z-scores can be positive or negative for data values above the mean of the distribution.