Business Statistics (True/ False)

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

False Explanation: A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are only two possible outcomes (success and failure), and in each trial the probability of a success (and failure) remains the same.

Both discrete and continuous variables may assume an uncountable number of values.

False Explanation: A discrete variable assumes a countable number of values because these values can be put in a sequence x1, x2, x3, and so on. Even if this sequence is infinite, its values can be counted as the first, the second, the third one, and so on. On the other hand, a continuous variable assumes any value from an interval, and such values cannot be counted (there are too many of them).

A qualitative variable assumes meaningful numerical values.

False Explanation: A quantitative variable assumes meaningful numerical values, while values of a qualitative variable are typically described in labels or names.

A risk-averse consumer ignores risk and makes his or her decisions solely on the basis of expected value.

False Explanation: A risk-averse consumer incorporates risk in his or her decision to accept a risky prospect.

Subjective probability is assigned to an event by drawing on logical analysis.

False Explanation: A subjective probability is calculated by drawing on personal and subjective judgment.

The complement of an event A, denoted by AC, within the sample space S, is the event consisting of all outcomes of A that are not in S.

False Explanation: Ac consists of all outcomes of S that are not in A.

Nominal and interval scales are used for qualitative variables.

False Explanation: An interval scale is used for quantitative variables, and the nominal scale is used for qualitative variables.

Chebyshev's theorem is only applicable for sample data.

False Explanation: Chebyshev's theorem is valid for both sample and population data. It is valid for all types of data sets including skewed and symmetric.

Cross-sectional data contain values of a characteristic of one subject collected over time.

False Explanation: Cross-sectional data contain values of a characteristic of many subjects at the same point or approximately the same point in time, or without regards to differences in time.

Events are exhaustive if they do not share common outcomes of a sample space.

False Explanation: Events are exhaustive if they include all outcomes in the sample space.

Joint probability of two independent events A and B equals the sum of the individual probabilities of A and B.

False Explanation: For independent events, the joint probability equals the product of the individual probabilities: P(A ∩ B) = P(A)P(B).

Geometric mean is greater than the arithmetic mean.

False Explanation: Geometric mean is smaller than the arithmetic mean and is less sensitive to outliers.

The branch of statistical studies called inferential statistics refers to drawing conclusions about sample data by analyzing the corresponding population.

False Explanation: Inferential statistics refers to drawing conclusions about a population from analyzing sample data.

Population parameters are used to estimate corresponding sample statistics.

False Explanation: Sample statistics are used to estimate the corresponding population parameter.

The expected value of simple information is the mean of a discrete probability distribution when the discrete random variable is expressed in term of dollars.

False Explanation: The expected value of simple information is the mean of a discrete probability distribution regardless of the term the variable is expressed.

The median is not always the 50th percentile.

False Explanation: The median is always the 50th percentile. If n is odd, L50 = (n + 1)/2 is an integer directly defining the unique middle position in the sorted data set. If n is even, L50 = (n + 1)/2 is the average of the two middle positions n/2 and n/2 + 1, and hence the median is the average of the corresponding two middle values.

The arithmetic mean is the middle value of a data set.

False Explanation: The median is the middle value of a data set.

The probability of a union of events can be greater than 1.

False Explanation: The probability can never exceed 1.

The total probability rule is defined as P(A) = P(A ∩ B) P(A ∩ Bc )

False Explanation: The total probability rule is defined as P(A) = P(A ∩ B) + P(A ∩ Bc ).

The zero point of an interval scale reflects a complete absence of what is being measured.

False Explanation: The zero point of an interval scale does not reflect a complete absence of what is being measured; the value of zero is arbitrary chosen.

For two independent events A and B, the probability of their intersection is zero.

False Explanation: Two independent events can happen simultaneously so they are not mutually exclusive events. The probability of their intersection is the two probabilities multiplied together. If two events are mutually exclusive, then probability of intersection is zero.

We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

False Explanation: We use the hypergeometric distribution in place of the binomial distribution when sampling without replacement from a population whose size N is not significantly larger than the sample size n.

Z-scores can always be used to detect outliers.

False Explanation: Z-scores can only be used to detect outliers when the data are relatively symmetric and bell-shaped.

The variance is an average squared deviation from the mean.

True

A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space.

True Explanation: A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space.

A binomial random variable is defined as the number of successes achieved in n trials of a Bernoulli process.

True Explanation: A binomial random variable is defined as the number of successes achieved in n trials of a Bernoulli process.

A continuous variable assumes any value from an interval (or collection of intervals).

True Explanation: A continuous variable is characterized by infinitely uncountable values and can take any value within an interval.

A risk-neutral consumer ignores risk and makes his or her decisions solely on the basis of expected value.

True Explanation: A customer who is risk-neutral doesn't care about risk. They just want to make sure they have an expectation of gain.

Bayes' theorem is used to update prior probabilities based on the arrival of new relevant information.

True Explanation: Bayes' theorem is a procedure for updating probabilities based on new information.

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

True Explanation: Descriptive statistics refers to the summary of important aspects of a data set.

Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes.

True Explanation: Events are exhaustive if they include all outcomes in the sample space. Mutually exclusive events do not share common outcomes of a sample space.

Outliers are extreme values above or below the mean that require special consideration.

True Explanation: Outliers are extremely small or large values.

Approximately 60% of the observations in a data set fall below the 60th percentile.

True Explanation: Percentile is defined as the approximate percentage of the observations have values below the percentile value.

A continuous random variable X assumes an (infinitely) uncountable number of distinct values.

True Explanation: The (infinitely) uncountable values cannot be put in a sequence. In particular, an interval has an uncountable number of values.

The empirical rule is only applicable for approximately bell-shaped data.

True Explanation: The empirical rule can be applied to the distribution that is relatively symmetric and bell-shaped.

The expected value of a random variable X can be referred to as the population mean.

True Explanation: The expected value of a discrete random variable is a weighted average of all possible values of X.

The standard deviation is the positive square root of the variance.

True Explanation: The standard deviation is the positive square root of the variance

Time series data contain values of a characteristic of a subject over time.

True Explanation: Time series can include hourly, daily, weekly, monthly, quarterly, or annual observations.

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

True Explanation: σ=√(σ2)

The intersection of two events A and B, denoted by A ∩ B, is the event consisting of all outcomes that are in A and B.

True Explanation: The intersection of two events is the event consisting of all outcomes in A and B.