STA3032 Engineering Stats Exam 1

A _____________ population consists of physical objects, while a _______________ population consists of values from a process under identical experimental conditions.

tangible, conceptual

The ______________________ of a continuous random variable X is Integral(-∞,∞)(x − µx)^2f(x)dx .

variance

Match the sampling method on the left with its description on the right. Methods: weighted sampling, stratified random sampling, cluster sampling Descriptions: (1) Items are drawn from the population in groups; (2) Some items are given a greater chance of being selected than others; (3) A population is divided into subpopulations, and a simple random sample is drawn from each subpopulation.

weighted (2), stratified (3), cluster (1)

The values of a ________________ random variable can be arranged in a (finite or infinite) sequence.

discrete

A histogram is perfectly ____________ if its right half is a mirror image of its left half.

symmetric

Order the steps for making a histogram. (On Exam 1, given a small data set and set of intervals, be able to sketch a histogram.) (1) Draw rectangles with heights equal to frequencies, relative frequencies, or densities for equal-width classes, or to densities for unequal widths. (2) Choose boundary points for the class intervals. (3) Compute the density for each class (optional for equal-width classes). (4) Compute the frequency and (optionally for equal-width classes) relative frequency for each class.

2, 4, 3, 1

The sample mean of the sample 2, 5, 1, 4 is _________________.

3

A ________________ is a sample chosen by a method in which each collection of items of the same size from the population is equally likely to make up the sample. (A) simple random sample (B) cluster sample (C) stratified sample (D) sample of convenience

A

A deck of 52 playing cards consists of four suits (clubs, diamonds, hearts and spades) of 13 cards each (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King). A randomly chosen card is drawn. The probability it is an even number (2, 4, 6, 8, or 10) or club is ____________________.(Answer with a reduced fraction.) (A) 7/13 (B) 5/52 (C) 5/13 (D) 33/52

A

A mountaineer attaches a backpack to two long pieces of nylon webbing of the same length, each wound on its own spool. Each spool contains a taped webbing joint having essentially zero strength with probability 0.1. One spool having a joint is independent of the other spool having a joint. The spools are unwound to lower the backpack off a tail cliff. What is the probability the backpack falls because both spools have a taped joint? (A) 0.01 (B) 0.19 (C) 0.99 (D) 0.2

A

An advantage of an observational study over a corresponding controlled experiment is that (A) the study can incorporate categorical data while the experiment cannot (B) the study may be practical where the experiment is not (C) the study can identify cause and effect where the experiment cannot

B

A rope splicing shop's splices are weak with probability 1/1000 and ugly with probability 1/20; and 2/3 of weak splices are ugly. In finding the probability that an ugly splice is weak, which of the following expressions is not correct? Choose the single INCORRECT response. (A) P(weak|ugly)P(ugly)/P(weak) (B) P(ugly and weak)/P(ugly) (C) P(ugly|weak)P(weak)/P(ugly)

A

A serious drawback of sample variance s^2 as a measure of spread is that __________________. (A) Its unit of measurement is not the same as the unit of sample values. (B) It cannot be negative. (C) It divides the sum of squared deviations from the sample mean by n − 1 instead of by n

A

For a random variable X and a constant b, the mean of X + b is ____________________. (A) µX + b (B) b × µX (C) µX (D) µx + |b|

A

For a random variable X with mean 5 and variance 4, the variance of X + 3 is _____________________. (A) 4 (B) 7 (C) 8 (D) 36

A

For events A and B, what is the set of outcomes that belong either to A, to B, or to both? (A) union (B) intersection

A

For the random variable X with probability density function f(x) = x/2 for 0 ≤ X ≤ 2 (and f(x) = 0 otherwise), P(X > 1) = _________________ (A) 3/4 (B) 1/4 (C) 4/3 (D) 1/2

A

Here are mutually exclusive outcomes of a particular quarterback throwing a pass, with associated probabilities: complete pass(1/2), incomplete pass(1/4), intersection (1/8). or fumble (1/8). (Treat these outcomes as mutually exclusive.) The probability of an outcome other than a complete pass is ________________________. (A) 1/2 (B) 3/4 (C) 1/8 (D) 7/8

A

If P(A) = 0.3, P(B) = 0.4, and P(B|A) = 0.4, then are A and B independent events? (A) Yes, A and B are independent. (B) No, A and B are dependent. (C) There is not enough information to say whether A and B are independent.

A

In today's weather forecast, the probability of rain is 1/2, the probability of lightning is 3/10, and the probability of lightning given rain is 2/5. Find the probability of rain and lightning. (A) 1/5 (B) 3/25 (C) 3/20 (D) 4/5

A

In today's weather forecast, the probability of rain is 1/2, the probability of lightning is 3/10, and the probability of lightning given rain is 2/5. Find the probability of rain given lightning. (A) 2/3 (B) 2/5 (C) 5/3 (D) 1/2

A

Suppose X, Y and Z are random variables with means µX = 3, µY = 4 and µZ = 5. Find the mean of W = X+2Y +Z. (A) 16 (B) 24 (C) 11 (D) 12

A

Suppose X1, X2, . . . , Xn is a random sample from a population with mean µ and variance σ^2 , with sample mean X¯. Then the mean of X¯ is (A) µ (B) µ/n (C) nµ

A

The ________________ of a continuous random variable X is Integral(-∞,∞)xf(x)dx . (A) expected value (B) variance (C) standard deviation (D) integral of the density

A

The great advantage of a properly designed and controlled experiment over an observational study is that ____________ (A) An experiment can produce reliable information about cause and effect. (B) Data collection is easier for an experiment than for an observational study. (C) An experiment is often practical where a corresponding observation study is not

A

The output of a rope splicing shop includes cosmetic defects in 1/10 of its single braid splices, 1/8 of its double braid splices, and 1/20 of its 16-strand splices. For a large order of splices, 1/3 are in single braid rope, 1/2 are in double braid rope, and 1/6 are in 16-strand rope. What is the probability of a cosmetic defect in a randomly-chosen splice from this order? (A) 0.104 (B) 0.275 (C) 0.896 (D) 0.0000174

A

True or false: A sample space contains all the possible outcomes of an experiment. (A) True (B) False

A

Two histograms share a horizontal axis indicating the range of the data in the two samples. The first histogram is entirely to the left of the second. Which of the following statements is true? Pick the single correct response. (A) The first sample mean is less than the second. (B) The first sample variance is less than the second. (C) The first sample standard deviation is less than the second.

A

Which of the following statements about the width of the class intervals in a histogram is correct? (A) Choosing a large number of class intervals will produce a narrow width. (B) There is generally only one right way to choose the number of class intervals. (C) Choosing a small number of class intervals will produce a narrow width.

A

Which of the following statements is true about the median of a sample of size n, where n is even. (A) The median is the average of the number in position n/2 and the number in the position (n/2) + 1. (B) The median is the number in the position (n + 1)/2. (C) The median is the average of the number in position n/2 and the number in the position (n/2) − 1.

A

Which statements are reasons to suspect that a sample is not a simple random sample? (A) Parts of the population were excluded before the sample was drawn. (B) The data points in the sample do not all have the same value. (C) A plot of the sample data shows an increasing or decreasing trend, oscillation, or another pattern.

A and C

A family is selected at random from a certain city. Let A be the event the family has at most two children, and let B be the event the family has at least two children. Are A and B mutually exclusive? (A) Yes (B) No

B

A sample of convenience may be acceptable when there is _______________ difference between the sample and the population. (A) a systematic (B) no systematic (C) no random

B

Suppose X1, X2, . . . , Xn is a random sample from a population with mean µ and variance σ^2 , with sample mean X¯. Then the variance of X¯ is (A) σ^2 (B) nσ2 (C) σ^2/n (D) σ^2/√n

C

Because of sampling variation that occurs between successive random samples from the same population, __________________ (A) random sampling is not useful. (B) two simple random samples from the same population may differ substantially. (C) measurement should be done on the entire population.

B

Because of sampling variation that occurs between successive random samples from the same population, _________________________ (A) random sampling is not useful. (B) two simple random samples from the same population may differ substantially. (C) measurement should be done on the entire population.

B

For a sample of categorical data, the _______________ for a given category is the number of sample items in that category divided by the sample size. (A) sample median (B) relative frequency (C) frequency (D) sample mean

B

Given that F1, . . . , Fn is a sample of Fahrenheit temperatures with sample mean F¯ = 50 and Ci = 5/9 (Fi − 32) are corresponding Celsius temperatures, C¯ = __________. (A) 14 (B) 10 (C) 18

B

If P(A) = 0.3, P(B) = 0.4, and P(B|A) = 0.4, then are A and B mutually exclusive? (A) Yes, A and B are mutually exclusive in this case. (B) No, A and B are not mutually exclusive in this case. (C) There is not enough information to say whether A and B are mutually exclusive.

B

Items in a simple random sample (SRS) are not independent because simple random sampling is done without replacement. However, a rule of thumb is that items in an SRS may be treated as independent if the sample size is no more than ______________ of the population size. (A) 1% (B) 5% (C) 10% (D) 20%

B

Suppose a die is rolled. Let E be the event that the number on the up-face is less than 4, and let F be the event that the number is a 2. True or False: E and F are independent events. (A) True (B) False

B

Suppose pencil lengths, in inches, are randomly distributed with mean 6.5 inches. There are 2.54 centimeters in 1 inch. What is the mean pencil length in centimeters? (A) 41.93 (B) 16.51 (C) 9.04 (D) 6.5

B

The probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw. What is the probability that he will break a chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing and 1/8 felling and bucking? (A) 0.052 (B) 0.01 (C) 0.99 (D) 0.00000003

B

The probability mass function of a discrete random variable X is p(x) = __________________________. (A) P(X < x) (B) P(X = x) (C) P(X ≥ x) (D) P(X ≤ x)

B

The relative frequency of a class in a histogram is _____________. (A) the sum of all the frequencies multiplied by the frequency of the class (B) the frequency of the class divided by the sum of all the frequencies (C) the sum of all the frequencies divided by the frequency of the class (D) the frequency of the class multiplied by the sum of all the frequencies

B

The sample standard deviation __________________. (A) has a unit of measurement that is the square root of the unit of the sample values. (B) has the same unit of measurement as the unit of the sample values. (C) is unitless. (D) has a unit of measurement that is the square of the unit of the sample values.

B

When an outlier identified in a data set, the best action is to _________________ (A) Delete it so that data analysis will proceed smoothly (B) Delete it only if it is very likely to be due to error (C) Ignore it and proceed with data analysis

B

Which of the following describes a population? (A) Statistic (B) Parameter

B

Which of the following phrases describe the shape of this histogram? Histogram of x ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ (A) Approximately symmetric (B) Skewed to the right (C) Skewed to the left

B

Which of the following statements is true about the median of a sample of size n, where n is odd? (A) The median is the average of the number is position n/2 and the number in position n/2 + 1 . (B) The median is the number in position n+1/2 . (C) The median is the average of the number in position n/2 and the number in position n/2 − 1 .

B

A fair coin is tossed twice. Which of the following represents a sample space for this experiment? Let H =Heads and T=Tails. (A) {HH, T T, HT} (B) {HH, T T, T H} (C) {HH, T T, HT, T H} (D) {H, T}

C

If X1 and X2 are independent random variables, each with variance σ^2 , find the variance of the variable Y = 1/2(X1 + X2). (A) σ^2 (B) 2σ^2 (C) (1/2)σ^2 (D) σ/√2

C

If a histogram is skewed to the left, then ___________________ (A) the right tail is the mirror image of the left tail (B) the right tail is approximately the same length as the left tail (C) the left tail is longer than the right tail (D) the right tail is longer than the left tail

C

In a density histogram, class density is equal to ________________. (A) Relative frequency/total number of points (B) Frequency/total number of points (C) Relative frequency/ class width (D) Frequency/class width

C

In a histogram with unequal class interval widths, the height of the rectangle for a class should be the class ______________. (A) Relative frequency (B) Frequency (C) Density

C

P(A), the ___________________ that event A occurs, is the proportion of times that event A would occur in the long run if the experiment were repeated many times. (Answer with one word) (A) proportion (B) possibility (C) probability (D) ratio

C

The events A and B are mutually exclusive if _________________ (A) their union is the sample space (B) their union is the larger of the two sets (C) their intersection is the empty set (D) their intersection is the sample space

C

The sample standard deviation of the sample X1, . . . , Xn is s = _________ (A) sqrt( (1/n) Sum(xi − x¯)^2 ) (B) 1/(n−1) Sum(xi − x¯)^2 (C) sqrt( 1/(n−1) Sum(xi − x¯)^2 ) (D) sqrt( 1/(n-1) Sum(xi − x¯) )

C

Which method produces a simple random sample of the population consisting of a day's production of 1000 network routers? (A) Use the first 25 routers completed after arrival of the quality engineer. (B) Use the 25 routers produced between 10:00 am and 11:00 pm. (C) Put the serial numbers 0001, 0002, . . . , 1000 on ping pong balls, shake them, and draw out 25. (D) Use the 25 routers with serial numbers 0040, 0080, . . . , 1000.

C

Which of the following are statistics? (A) The average number of children is a United States family is 1.86. (B) In a certain town, 30% of the residents are under the age of 18. (C) In a survey of college students, 42% said they went to the movies more than once in the past month.

C

Which of the following is a parameter? (A) In a recent survey, 62% of drivers said they were concerned about higher gas prices. (B) In a poll of voters, 53% of them supported the incumbent mayor for reelection. (C) Forty-seven percent of the residents of Central City own their homes.

C

1/10 of the first names of students in a class start with the letter "R", 1/8 start with "S", and 1/5 start with "T". The probability that a randomly chosen students's first name will start with "R" or "T" is ______________________. (A) 7/25 (B) 1/50 (C) 7/8 (D) 3/10

D

If X is a random variable and a is a constant, the standard deviation of aX is σaX = ___________________. (A) aσX (B) σX (C) a^2σX (D) |a|σX

D

The variance of a random variable X with probability density function f(x) = 2x for 0 ≤ x ≤ 1 (and f(x) = 0 otherwise) is what? (A) 0 (B) 1/9 (C) 2/3 (D) 1/18

D

Match each data type on the left with its description on the right. Data type: Numerical, categorical Description: (1) Sample items are placed in categories so that a category name is assigned to each item, (2) A number indicating how much or how many is assigned to each item in a sample.

Numerical (2), categorical (1)

Given that X1, . . . , Xn is a sample, a and b are constants, and Yi = a + bXi , match each quantity on the left with its value on the right. Quantities: Y¯ , sY^2 , sY Values: b^2sX^2, |b|sx, a + bX¯

Y¯ = a + bX¯, sY^2 = b^2sX^2, sY = |b|sx

Order the steps for making a boxplot from a sample, given median M, first quartile Q1, third quartile Q3, and interquartile range IQR = Q1 − Q3. Place these in the proper order. (On Exam 1, given a small dataset, be able to sketch a boxplot.) a. Draw a vertical scale. b. Draw vertical lines to complete a box between Q1 and Q3. c. Draw vertical lines from box top to the largest value no more than Q3+1.5 IQR and from box bottom to the smallest value no less than Q1-1.5IQR. d. Draw horizontal lines at M, Q1, and Q3. e. Points outside the range of vertical lines are outliers; plot them individually.

a, d, b, c, e

Data for which each item consists of two values are called _____________________.

bivariate

The ______________________ of an event A is the set of outcomes in the sample space that do not belong to A.

complement

The probabilities of a _____________ random variable are given by areas under a curve called its probability density function.

continuous

To make a ______________ , label a horizontal number line over the range of the data. For each distinct data value, add a vertical column of dots, with the number of dots equal to the value's frequency in the sample.

dotplot

The 25th percentile is the _____________ quartile.

first

Match each statistic for a sorted sample of size n on the left with its rough description on the right. (On Exam 1, given a small dataset, be able to compute these statistics.) Statistics: first quartile, median, third quartile, maximum, minimum Descriptions: (1) value at position 3(n+1)/4 , (2) value at position 1, (3) value at position n+1/4 , (4) value at position n, (5) value at position n+1/2

first quartile, (3); median (5); third quartile (1); maximum (4); minimum (2)

For a sample of categorical data, the ______________________ for a given category is the number of sample items in that category.

frequency

Two random variables X and Y are ____________________ if, for all sets of numbers S and T, P(X ∈ S and Y ∈ T) = P(X ∈ S)P(Y ∈ T).

independent

The _________________ of events A and B is the set of outcomes that belong both to A and to B.

intersection

The 50th percentile is the same as the __________________.

median

The _________________ of a continuous random variable X is the point xm such that P(X ≤ xm) = 0.5.

median

An _______________ is a data point much larger or smaller than the others in its data set.

outlier

The p^th __________________ of a sample size n is the value at position (p/100)(n + 1) in the sorted sample, or the average of the two values on either side if this position is not an integer.

percentile

A _______________ is the entire collection of individuals about which information is sought.

population

The relative frequency of a class in a histogram is the _______________ of observations that are in the class.

proportion

A _________________ is a subset of a population containing the objects or outcomes that are actually observed.

sample

A ___________________ is a two-dimensional plot of a numerical bivariate data set (x1, y1), . . . ,(xn, yn).

scatterplot

A ___________________ is a number that describes a sample.

statistic