277 Exam 1
A point estimate is a function of the random sample used to make inferences about the value of an unknown population parameter. A point estimator reflects the actual value of the point estimate derived from a given sample.
False - it does not provide an exact value
An unbiased estimator is efficient if its standard error is higher than that of other unbiased estimators of the estimated population parameter.
False unbiased is never efficient
What is the interquartile range?
Q1-Q3
The empirical rule is only applicable for approximately bell-shaped data.
True
continuous random variable
can assume any value in an interval on the real line or in a collection of intervals. -It is not possible to talk about the probability of the random variable assuming a particular value. -Instead, we talk about the probability of the random variable assuming a value within a given interval.
Examples of random variables that closely follow a normal distribution include the age and the class year designation of a college student.
false
If you are not given a population size it is then
infinite
Which of the following statements about the mean absolute deviation (MAD) is most accurate? MAD:
is denominated in the same units as the original data.
The advantage of using mean absolute deviation rather than variance as a measure of dispersion is that mean absolute deviation:
is less sensitive to extreme deviations.
Sample statistic are
variable
What is/are characteristic(s) of the geometric mean?
. It is always less than or equal to the arithmetic mean.
Chebyshev's theorem is applicable when the data are
Any shape
What is the difference between Chebyshev's theorem and the empirical rule?
Chebyshev's theorem applies to all data sets, whereas the empirical rule is only appropriate when the . data have approximately a symmetric and bell-shaped distribution.
p bar is not a population parameter
just know it
For k > 1, Chebyshev's theorem is useful in estimating the proportion of observations that fall within:
k standard deviations from the mean. 1 - 1/k^2
If we are told that population is normal then sampling distribution will be ________ no matter what
normal can use any sample size
date gathered from a sample is used to make a
point estimation
A census is an example of
population data
Stratified random sampling
population is divided into groups or strata and then a random sample is taken from each group
Cluster Sample
population is divided into groups, groups are randomly elected and sample is taken rom entire group
Point estimation estimates a -
population parameter
The mean and standard deviation of the continuous uniform distribution are equal.
false
In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to .
A number of randomly occurring events that are part of the production process.
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.
The MAD is a less effective measure of variation when compared with the average deviation from the mean.
False
The arithmetic mean is the middle value of a data set.
False
The letter Z is used to denote a random variable with any normal distribution.
False
The median is not always the 50th percentile.
False
The variance and standard deviation are the most widely used measures of central location.
False
We calculate a parameter to make inferences about a statistic.
False
Successful firms must focus on the quality of the products and services that they offer. Which factor(s) contributes to the quest for quality?
Global competition Consumer expectations Technological advances
Selection bias occurs when .
Portions of the population are excluded from the consideration for the sample
What can be said about the expected value and standard deviation of an exponential distribution?
The expected value is equal to the standard deviation.
In its standard form, Chebyshev's theorem provides a lower bound on:
The proportion (or percentage) of observations lying within a certain interval.
According to the central limit theorem, the distribution of the sample means is normal if .
The sample size n > 30
What is the relationship between the variance and the standard deviation?
The standard deviation is the positive square root of the variance.
What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?
The tails get closer and closer to the x axis but never touch it.
Bias can occur in sampling. Bias refers to .
The tendency of a sample statistic to systematically over- or underestimate a population parameter
What capabilities do Chebyshev's theorem and the empirical rule provide?
They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.
Nonresponse bias occurs when .
Those responding to a survey or poll differ systematically from the non-respondents
Is it possible for a data set to have no mode?
Yes, if there are no observations that occur more than once.
The covariance between the returns on two assets is negative. This occurs when:
on average, the return on one asset is below its expected value and the return on the other asset is above its expected value.
The probability density function of a normal distribution is in general characterized by being symmetric and bell-shaped.
true
What is/are the characteristic(s) of the coefficient of variation?
- It adjusts for differences in the magnitude of means. - It allows for direct comparisons across different data sets.
The probability that a normal random variable is less than its mean is
.5
How many parameters are needed to fully describe any normal distribution?
2
Consider the following data: 1, 2, 4, 5, 10, 12, 18. The 30th percentile is closest to
2.8
How do we find the median if the number of observations in a data set is odd?
Taking middle number in sorted data set
When using the empirical rule, which assumption is made?
The data is approximately symmetric and bell-shaped.
What does the covariance measure?
The direction of a linear relationship between two variables.
The Sharpe ratio measures
The extra reward per unit of risk
Which of the following is most influenced by outliers?
Arithmetic mean
The median is defined as...
Middle point of a data set
A population consists of all items of interest in a statistical problem.
True
what is considered an estimator
X bar
Parameters are
Constant
Mean-variance analysis suggests that investments with lower average returns are also associated with higher risks.
False
What is an advantage of the correlation coefficient over the covariance?
- It falls between -1 and 1. - It is a unit-free measure, therefore making it easier to interpret.
Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
False
.Which of the following relationships may be concluded from examining the correlation coefficient?
- No relationship - A positive relationship - A negative relationship
Calculate the interquartile range from the following data: 1, 2, 4, 5, 10, 12, 18.
12-2 =10 Remember when there is an odd number you just use median of both sides
The covariance between the returns of A and B is -0.112. The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is closest to:
-0.53
The covariance between the returns of stock A and stock B is -125. The standard deviation of the rates of return is 20 for stock A and 10 for stock B. The correlation coefficient of the rates of return between A and B is closest to:
-0.625
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
For any normally distributed random variable with mean μ and standard deviation σ, the proportion of the observations that fall outside the interval [μ - σ, μ + σ] is closest to .
.3174
The probability density function of a continuous uniform distribution is positive for all values between -∞ and +∞.
False
Sales for Adidas grew at a rate of 0.5196 in 2006, 0.0213 in 2007, 0.0485 in 2008, and -0.0387 in 2009. The average growth rate for Adidas during these four years is closest to:
11.83%
The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. Find the mean and standard deviation of the waiting time.
115 seconds and 49.07 seconds
Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. Refer to Exhibit 7-1. What is the expected value for the sampling distribution of the number of school days missed due to influenza?
28
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 .
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 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.
uniformly distributed
A random variable is uniformly distributed whenever the probability is proportional to the interval's length.
The coefficient of variation is best described as
A relative measure of dispersion. -indicates how large the standard deviation is in relation to the mean
When applicable, the empirical rule provides the approximate percentage of observations that fall within how many standard deviations from the mean?
A. 1, 2, or 3 standard deviations
The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is .
A. 1/(b - a) between a and b, and zero otherwise
. 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. A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. B. A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. C. The z value corresponding to x = μ is zero. D. All of the above
If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?
A. For any sample size n, the sampling distribution of the sample mean is normally distributed.
Which of the following statements is most accurate when defining percentiles
Approximately (100-p)% of the observations are greater than the pth percentile.
Chebyshev's theorem is only applicable for sample data.
False
Cumulative distribution functions can only be used to compute probabilities for continuous random variables.
False
Which of the following is true about statistics such as the sample mean or sample proportion?
D. A statistic is a random variable.
For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed.
False
Given that the probability distribution is normal, it is completely described by its mean μ > 0 and its standard deviation σ > 0.
False
A local company makes snack size bags of potato chips. The company produces batches of 400 snack size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the population of filling weights is normally distributed with a standard deviation of 0.1 ounces. The company periodically weighs samples of 10 bags to ensure the proper filling process. The last five sample means, in ounces, were 1.99, 2.02, 2.07, 1.96, and 2.01. Is the production process under control?
D. Yes, since the sample means fall within the upper and lower control limits
The detection approach to statistical quality control .
Determines at which point the production process does not conform to specifications
A parameter is a random variable, whereas a sample statistic is a constant.
False
A sample consists of all items of interest in a statistical problem, whereas a population is a subset of the population. We calculate a parameter to make inferences about the unknown sample statistic.
False
In what way(s) is the concept of geometric mean useful?
In evaluating investment return In calculating average growth rates
Which of the following is not a form of bias?
Information from the sample is typical of information in the population.
Acceptance sampling is a(n) .
Inspection of a portion of the products at the completion of the production process.
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
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.
The finite correction factor is always .
Less than one, and therefore decreases the standard deviations of and assumption of infinite population computed under the
How do you define the range?
Max - Min
The Boom company has recently decided to raise the salaries of all employees by 10 percent. Which of the following is (are) expected to be affected by this raise?
Mean median and mode
Mean of 7
Median will be less than 7
Which five values are graphed on a box plot?
Min, Quartile 1, Median, Quartile 3, Max
The continuous uniform distribution describes a random variable, defined on the interval [a, b], that has an equally likely chance of assuming values within any subinterval of [a, b] with the same length.
True
The geometric mean is a multiplicative average of a data set.
True
The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.
True
The probability density function of a continuous random variable can be regarded as a counterpart of the probability mass function of a discrete random variable.
True
The standard deviation is the positive square root of the variance.
True
The standard deviation of equals the population standard deviation divided by the square root of the sample size, or equivalently
True
The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.
True
The standard normal table is also referred to as the z table.
True
The mode is defined as...
The most frequent value in a data set.
The terms central location or central tendency refer to the way quantitative data tend to cluster around some middle or central value.
True
The variance is an average squared deviation from the mean.
True
When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.
True
What is (are) the most widely used measure(s) of dispersion?
Variance and standard deviation - relates to variability
.A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.
True
A box plot is useful when comparing similar information gathered at different places or times.
True
A continuous random variable is characterized by uncountable values and can take on any value within an interval.
True
An estimator is consistent if it approaches the estimated population parameter as the sample size grows larger.
True
An estimator is unbiased if its expected value equals the estimated population parameter.
True
Approximately 60% of the observations in a data set fall below the 60th percentile.
True
Bias refers to the tendency of a sample statistic to systematically over- or underestimate a population parameter.
True
If we had access to data that encompass the entire population, then the values of the parameters would be known and no statistical inference would be needed.
True
In a data set, an outlier is a large or small value regarded as an extreme value in the data set.
True
Nonresponse bias occurs when those responding to a survey or poll differ systematically from the non- respondents.
True
The Sharpe ratio measures the extra reward per unit of risk.
True
The coefficient of variation is a unit free measure of dispersion.
True
The empirical rule can be used to estimate some proportions when data has what shape?
When it is approximately symmetric and bell-shaped
Which of the following statements about variance is most accurate? Variance:
Which of the following statements about variance is most accurate? Variance:
Is it possible for a data set to have more than one mode?
Yes, if two or more values in a data set occur with the most frequency and the frequency is greater than one.
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
For any population with expected value μ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when .
false
Just as in the case of the continuous uniform distribution, the probability density function of the normal distribution may be easily used to compute probabilities.
false
We are often interested in finding the probability that a continuous random variable assumes a particular value.
false
For any population proportion p, the sampling distribution of will be approximately normal if the sample size n is sufficiently large. As a general guideline, the normal distribution approximation is justified when and .
true
In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.
true
The area under the graph and probability are :
identical - valid for all continous random variable
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
A simple random sample is a sample of n observations which has the same probability of being selected from the population as any other sample of n observations.
true
Which of the following is an example of a sample statistic?
x bar
Which of the following is considered an estimate?
x bar