Statistics Questions
Each salesperson in a large department store chain is rated on his or her sales ability and potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. Potential for Advancement Fair Good Excellent Sales ability Below average 16 12 22 Average 45 60 45 Above average 93 72 135 What is the probability that a salesperson selected at random will have below-average sales ability and fair potential for advancement?
0.032
Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-ounce bottle of Midnight, a feminine shaving kit, a raincoat, or a pair of rain boots. If you purchased Allure, what is the probability you randomly select an umbrella and a shaving kit in that order?
0.05
In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who did NOT attend college?
0.08
In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety percent of the females attended college; 78% of the males attended college. A management trainee is selected at random. What is the probability that the person selected is a female who attended college?
0.72
An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight. Weight % of Total Underweight 2.5 Satisfactory 90.0 Overweight 7.5 What is the probability of selecting three packages that are satisfactory?
0.729
The variance of a sample of 121 observations equals 441. The standard deviation of the sample equals
21
Ages Frequency 40 up to 50 10 50 up to 60 28 60 up to 70 12 What is the Class Interval?
10
What does 6!2! / 4!3!
10
An electronics firm sells four models of stereo receivers, three amplifiers, and six speaker brands. When the four types of components are sold together, they form a "system." How many different systems can the electronics firm offer?
72
The 50th percentile of a distribution is the same as the distribution mean.
False
The order in which runners finish in a race would be an example of continuous data.
False
The variance is the mean of the sum of the squared deviations between each observation and the median.
False
When TV advertisements report that "2 out of 3 dentists surveyed indicated they would recommend Brand X toothpaste to their patients," an informed consumer may question the conclusion because
The advertisement does not include the number of dentists surveyed
A student was interested in the cigarette-smoking habits of college students and collected data from an unbiased random sample of students. The data are summarized in the following table: Males 50 Females 75 Males who smoke 20 Males who do not smoke 30 Females who smoke 25 Females who do not smoke 50 What is wrong with this frequency table?
The classes are not mutually exhaustive
To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial.
True
To infer something about a population, we usually take a sample from the population.
True
A pie chart shows the
relative frequencies of a qualitative variable.
In a contingency table, we describe the relationship between ________.
two variables, one measured as an ordinal variable and the other as a ratio variable
The "box" in a box plot shows the interquartile range.
True
What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, a median of 12, and a standard deviation of 6?
+2.5
The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147, and $136. What is the range?
$17
The sample variance of hourly wages was 10. What is the sample standard deviation?
$3.16
During the past six months, a purchasing agent placed the following three orders for coal: Tons of Coal 1,200 3,000 500 Price Per Ton $ 28.50 $ 87.25 $ 88.00 What is the weighted arithmetic mean price per ton?
$72.33
Refer to the following wage breakdown for a garment factory: Hourly Wages Number of employees $6 up to $7 18 7 up to 10 36 10 up to 13 20 13 up to 16 6 What is the class midpoint for the class with the greatest frequency?
$8.50
For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
(n + 1) / 2
What is the possible range of values for Pearson's coefficient of skewness?
-3 and +3
Refer to the following distribution of ages: Ages Frequency 40 up to 50 10 50 up to 60 28 60 up to 70 12 For this distribution of ages, what is the relative class frequency for the lowest class?
0.2
A group of 100 students was surveyed about their interest in a new International Studies program. Interest was measured in terms of high, medium, or low. In the study, 30 students responded high interest, 40 students responded medium interest, and 30 students responded low interest. What is the relative frequency of students with high interest?
0.3
Each salesperson in a large department store chain is rated on his or her sales ability and potential for advancement. The data for the 500 sampled salespeople are summarized in the following table. Potential for Advancement Fair Good Excellent Sales ability Below average 16 12 22 Average 45 60 45 Above average 93 72 135 What is the probability that a salesperson selected at random will have an excellent potential for advancement given he or she also has above-average sales ability?
0.45
A study of 200 computer service firms revealed these incomes after taxes: Income After Taxes Number of Firms Under $1 million 102 $1 million up to $20 million 61 $20 million or more 37 What is the probability that a particular firm selected has $1 million or more in income after taxes?
0.49
The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1986 to $5,100 million in 2009. What is the geometric mean annual percent increase in international passenger revenues?
10.4
Refer to the following distribution of commissions: Monthly Commissions Class Frequencies $600 up to $800 3 800 up to 1,000 7 1,000 up to 1,200 11 1,200 up to 1,400 12 1,400 up to 1,600 40 1,600 up to 1,800 24 1,800 up to 2,000 9 2,000 up to 2,200 4 For the preceding distribution, what is the midpoint of the class with the greatest frequency?
1500
Refer to the following distribution of ages: Ages Frequency 40 up to 50 10 50 up to 60 28 60 up to 70 12 What is the class midpoint of the highest class?
65
A sample of experienced typists revealed that their mean typing speed is 87 words per minute and the median typing speed is 73 words per minute. The standard deviation of typing speed is 16.9 words per minute. What is the Pearson coefficient of skewness?
2.5+
Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester?
2.76
Refer to the following information from a frequency distribution for heights of college women recorded to the nearest inch: the first two class midpoints are 62.5" and 65.5". What is the class interval?
3
A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?
3
Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. Length of Time (in minutes) Number 1 up to 4 4 4 up to 7 8 7 up to 10 14 10 up to 13 9 13 up to 16 5 16 up to 19 2 What is the standard deviation (in minutes)?
3.89
Refer to the following breakdown of responses to a survey of room service in a hotel: Response Frequency Not satisfied 20 Satisfied 40 Highly satisfied 60 What percentage of the responses indicated that customers were satisfied?
33%
The sum of the deviations from the mean for the set of numbers 4, 9, and 5 will equal zero.
True
Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean annual percent increase?
5.5
Refer to the following distribution: Cost of Textbooks Frequency $25 up to 35 2 35 up to 45 5 45 up to 55 7 55 up to 65 20 65 up to 75 16 What is the class midpoint for the $45 up to $55 class?
50
You are assigned to design color codes for different parts. Three colors are used to code on each part. Once a combination of three colors is used—such as green, yellow, and red—these three colors cannot be rearranged to use as a code for another part. If there are 35 combinations, how many colors are available?
7
The number of students at a local university increased from 2,500 students to 5,000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of
7.2 percent per year
The number of employees less than(!) the upper limit of each class at Lloyd's Fast Food Emporium is shown in the following table: Ages Cumulative Number 18 up to 23 6 23 up to 28 19 28 up to 33 52 33 up to 38 61 38 up to 43 65 What is it called?
A Cumulative Frequency Distribution
Refer to the following breakdown of responses to a survey of "Are you concerned about being tracked while connected to the Internet?" Response Frequency Very concerned 140 Somewhat concerned 40 No concern 20 What type of chart should be used to describe the frequency table?
A bar chart
Refer to the following breakdown of responses to a survey of room service in a hotel: Response Frequency Not satisfied 20 Satisfied 40 Highly satisfied 60 What type of chart should be used to describe the frequency table?
A bar chart
Very confident 63 Somewhat confident 135 Not very confident 99 Don't know 3 What type of chart should be used to show relative class frequencies?
A pie chart
Extremely high or low scores affect the value of the median.
False
The relative frequency for a class represents the
Percentage of observations in a class
Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as
Bimodal (having two modes)
When computing the arithmetic mean, the smallest value in the data set
Can be any value
If a student places in the 99th percentile on an exam, she performed better than 99% of all students who completed the exam. Her performance is similar to a statement based on a __________.
Cumulative Frequency Distribution
What type of variable is "pounds of popcorn" served at a movie theater?
Continuous
What type of variable is the number of gallons of gasoline pumped by a filling station during a day?
Continuous
The average number of passengers on commercial flights between Chicago and New York City is an example of a statistic.
True
In order to convert class frequency to relative class frequency, we
Divide the frequency of the class by the sample size
Bayes' theorem is used to calculate a subjective probability.
False
A combination of a set of objects is defined by the order of the objects.
False
The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of its occurrence.
True
The probability of two or more events occurring concurrently is called a(n) _______.
Joint Probability
A marketing class of 50 students evaluated the instructor using the following scale: superior, good, average, poor, or inferior. The descriptive summary showed the following survey results: 2% superior, 8% good, 45% average, 45% poor, and 0% inferior.
Most students rated the professor as poor or average
A survey includes a question about marital status that has the following responses: single, married, divorced, separated, or widowed. What is the scale of measurement for this question?
Nominal
If Gallup, Harris, and other pollsters asked people to indicate their political party affiliations as Democrat, Republican, or independent, the data gathered would be an example of which scale of measurement?
Nominal
The Equal Employment Opportunity Act requires employers to classify their employees by gender and national origin. Which level of measurement is this?
Nominal
A group of women tried five brands of fingernail polish and ranked them according to preference. What level of measurement is this?
Ordinal
The final rankings of the top 20 NCAA college basketball teams are an example of which level of measurement?
Ordinal
What type of variable is the number of robberies reported in your city?
Quantitative
The length of a bridge, measured in meters, is an example of
Quantitative Data
A small sample of computer operators shows monthly incomes of $1,950, $1,775, $2,060, $1,840, $1,795, $1,890, $1,925, and $1,810. What are these ungrouped numbers called?
Raw data
A table summarizing a set of data showing the fraction of the total number of items in several classes is a
Relative Frequency Table
The following table is a ________. 1 2 3 2 2 5 5 2 677 8 2 889 11 3 001 (6) 3 222233 7 3 555 4 3 667 1 3 9
Stem and Leaf Plot
The joint probability of two events, A and B, that are NOT independent is computed as P(A and B) = P(A) × P(B|A).
True
The joint probability of two independent events, A and B, is computed as P(A and B) = P(A) × P(B).
True
The number of children in a family is a discrete variable.
True
Which is true for a binomial distribution?
The probability of success remains the same from trial to trial.
What is the relationship among the mean, median, and mode in a symmetric distribution?
They're all equal
The 75th percentile is referred to as the ________.
Third Quartile
A joint probability measures the likelihood that two or more events will happen concurrently.
True
A population is a collection of all individuals, objects, or measurements of interest.
True
A sample is a portion or part of the population of interest.
True
A scatter diagram of sales versus production is labeled with sales on the Y-axis and production on the X-axis.
True
A stem-and-leaf diagram shows the actual data values.
True
An ordinal level of measurement implies some sort of ranking.
True
Data measured on a nominal scale can only be classified into categories.
True
If a distribution is negatively skewed, the distribution is not symmetrical and the long tail is to the left.
True
If there are "m" ways of doing one thing, and "n" ways of doing another thing, the multiplication formula states that there are (m) × (n) ways of doing both.
True
In a stem-and-leaf display, the leaf represents the members of a class in a frequency distribution.
True
Statistics is defined as a body of techniques used to facilitate the collection, organization, presentation, analysis, and interpretation of information for the purpose of making better decisions.
True
When data are collected using a quantitative, ratio variable, what is true about a frequency distribution that summarizes the data?
Upper and lower classes must be calculated
What is the relationship between the variance and the standard deviation?
Variance is the square of the standard deviation.
A dot plot is best applied when _____________________.
a single variable is summarized
The range of the coefficient of skewness is ____________.
both positive and negative values
When an experiment is conducted "without replacement," _______.
events are dependent
The sample mean
is found by adding all data values and dividing them by n.
If the variance of the "number of daily parking tickets" issued is 100, the standard deviation is defined as the _______.
square root of the variance of the "number of daily parking tickets"
A dot plot shows ____________.
the general shape of a distribution
A box plot shows ___________.
the relative symmetry of a distribution for a set of data
The 67th percentile is ________.
the value below which 67% of the observations occur
There are 10 AAA batteries in a box and 3 are defective. Two batteries are selected without replacement. What is the probability of selecting a defective battery followed by another defective battery?
⅟15 or about 0.07