Questions and Answers of Statistics Informed Decisions Using Data

This section consists of some true/false questions regarding concepts of statistical inference. Indicate whether a statement is true or false and, if false, indicate what is required to make the
The following sample was taken from a normally distributed population with a known standard deviation σ = 4. Test the hypothesis that the mean μ = 20 using a level of significance of 0.05 and the
A note on your results states “z = 1:87:” Calculate the p value assuming: (a) H: >Ho (b) H: (b) H:
In testing the null hypothesis that p = 0:3 against the alternative that p ≠ 0:3, the probability of a type II error is ______ when the true p = 0:4 than when p = 0:6. (1) the same (2)
In a hypothesis test the p value is 0.043. This means that we can find statistical significance at: (1) both the 0.05 and 0.01 levels (2) the 0.05 but not at the 0.01 level (3) the 0.01 but not at
An article states “there is no significant evidence that median income increased.” The implied null hypothesis is: (1) Median income increased. (2) Median income changed. (3) Median income did
A probability experiment consists of rolling a single fair die.(a) Identify the outcomes of the probability experiment.(b) Determine the sample space.(c) Define the event E = “roll an even
The data in Table 2 represent the results of a survey in which 200 people were asked their means of travel to work.(a) Use the survey data to build a probability model for means of travel to work.(b)
A pair of fair dice is rolled. Fair die are die where each outcome is equally likely.(a) Compute the probability of rolling a seven.(b) Compute the probability of rolling “snake eyes”; that is,
Sophia has three tickets to a concert, but Yolanda, Michael, Kevin, and Marissa all want to go to the concert with her. To be fair, Sophia randomly selects the two people who can go with her.(a)
Suppose that a survey asked 500 families with three children to disclose the gender of their children and found that 180 of the families had two boys and one girl.(a) Estimate the probability of
(a) Simulate the experiment of sampling 100 three-child families to estimate the probability that a three-child family has two boys.(b) Simulate the experiment of sampling 1000 three-child families
Our number system consists of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Because we do not write numbers such as 12 as 012, the first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8,
Suppose that a single card is selected from a standard 52-card deck, such as the one shown in Figure 9.(a) Compute the probability of the event E = “drawing a king.”(b) Compute the probability of
Suppose a single card is selected from a standard 52-card deck. Compute the probability of the event E = “drawing a king” or F = “drawing a diamond.”Approach The events are not disjoint
Using the data in Table 6,(a) Determine the probability that a randomly selected U.S. resident 15 years old or older is male.(b) Determine the probability that a randomly selected U.S. resident 15
According to the National Gambling Impact Study Commission, 52% of Americans have played state lotteries. What is the probability that a randomly selected American has not played a state
The data in Table 7 represent the income distribution of households in the United States in 2013.Compute the probability that a randomly selected household earned the following incomes in 2013:(a)
If P(E) = 0.55, P(E or F) = 0.70, and P(E and F) = 0.15, find P(F).
If P(F) = 0.30, P(E or F) = 0.65, and P(E and F) = 0.15, find P(E).
The following data represent the number of live multiple-delivery births (three or more babies) in a particular year for women 15 to 54 years old.(a) Determine the probability that a randomly
Birthdays Exclude leap years from the following calculations:(a) Compute the probability that a randomly selected person does not have a birthday on December 6.(b) Compute the probability that a
According to a study, the probability that a randomly selected person has hearing problems is 0.149. The probability that a randomly selected person has vision problems is 0.085. Can we compute the
According to a survey, the probability that a randomly selected worker primarily rides a bicycle to work is 0.792. The probability that a randomly selected worker primarily takes public
Cigar Smoking The data in the following table show the association between cigar smoking and death from cancer for 139,704 men. Note: Current cigar smoker means cigar smoker at time of death.(a) If
A university conducted a survey of 366 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank.(a) If a survey participant is
Driver Fatalities The data in the table represent the number of drivers involved in fatal crashes in a certain region by day of the week and gender.(a) Determine the probability that a randomly
Go to the book’s website to obtain the data file SullivanStatsSurveyI using the file format of your choice for the version of the text you are using. The data represent the results of a survey
In the game of roulette, the wheel has slots numbered 0, 00, and 1 through 36.A metal ball rolls around a wheel until it falls into one of the numbered slots. What is the probability that the ball
The probability that a randomly selected 24-year-old male will survive the year is 0.9986 according to the National Vital Statistics Report, Vol. 56, No. 9.(a) What is the probability that three
Compute the probability that at least one male out of 1000 aged 24 years will die during the course of the year if the probability that a randomly selected 24- year old male survives the year is
Suppose that E and F are two events and that N(E and F) = 210 and N(E) = 330. What is P(F|E)?
Suppose events E and F are disjoint. What is P(E and F )?
Determine whether the events E and F are independent or dependent. Justify your answer.(a) E: A person living at least 70 years.F: The same person regularly handling venomous snakes.(b) E: A
Suppose that events E and F are independent, P(E) = 0.3 and P(F) = 0.8. What is P(E and F)?
Suppose that events E and F are independent, P(E) = 0.4 and P(F) = 0.8. What is P(E and F)?
What is the probability of obtaining eleven tails in a row when flipping a coin? Interpret this probability.
About 5% of the population of a large country is math-phobic. If two people are randomly selected, what is the probability both are math-phobic? What is the probability at least one is math-phobic?
A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject). The
The probability that a randomly selected 1-year-old male chipmunk will live to be 2 years old is 0.97853.(a) What is the probability that two randomly selected 1-yearold male chipmunks will live to
A grocery bag can be classified as either paper or plastic. 96% of grocery bags are classified as plastic.(a) Two grocery bags are chosen at random. What is the probability that both grocery bags are
Suppose Nate loses 41% of all thumb wars.(a) What is the probability that Nate loses two thumb wars in a row?(b) What is the probability that Nate loses six thumb wars in a row?(c) When events are
Among 52- to 57-year-olds, 29% say they have danced in public while under the influence of alcohol.Suppose five 52- to 57-year-olds are selected at random.(a) What is the probability that all five
For the fiscal year 2007, a tax authority audited 1.65% of individual tax returns with an income of $$100$,000 or more. Suppose this percentage stays the same for the current tax year. What is the
Suppose a single die is rolled. What is the probability that the die comes up three? Now suppose that the die is rolled a second time, but we are told the outcome will be an odd number. What is the
The data in Table 8 on the previous page represent the marital status and gender of the residents of the United States aged 15 years old or older in 2013.(a) Compute the probability that a randomly
Suppose that 12.7% of all births are preterm. (The gestation period of the pregnancy is less than 37 weeks.) Also 0.22% of all births resulted in a preterm baby who weighed 8 pounds, 13 ounces or
The probability that a driver who is speeding gets pulled over is 0.8. The probability that a driver gets a ticket, given that he or she is pulled over, is 0.9. What is the probability that a
Suppose that of 100 circuits sent to a manufacturing plant, 5 are defective. The plant manager receiving the circuits randomly selects 2 and tests them. If both circuits work, she will accept the
In a study to determine whether preferences for self are more or less prevalent than preferences for others, researchers first asked individuals to identify the person who is most valuable and
Suppose that E and F are two events and that N(E and F) = 480 and N(E) = 810. What is P(F | E)?
Suppose that E and F are two events and that N(E and F) = 340 and N(E) = 550. What is P(F|E)?
Suppose that E and F are two events and that P(E) = 0.7 and P(F|E) = 0.8. What is P(E and F)?
The probability that a randomly selected individual in a country earns more than $$75$,000 per year is 7.5%. The probability that a randomly selected individual in the country earns more than
For the month of June in a certain city, 87% of the days are cloudy. Also in the month of June in the same city, 73% of the days are cloudy and foggy. What is the probability that a randomly selected
According to a recent study, 8.7% of high school dropouts are 16- to 17-year-olds. In addition, 6.3% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly
The data represent the number of driving fatalities for a certain area by age for male and female drivers.(a) What is the probability that a randomly selected driver fatality who was male was 16 to
Suppose you just received a shipment of nine televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is
This past semester, a professor had a small business calculus section. The students in the class were Jinita, William, Al, Allison, Pam, Mike, Neta, and Jim. Suppose the professor randomly selects
Suppose you just purchased a digital music player and have put 6 tracks on it.After listening to them you decide that you like 2 of the songs.With the random feature on your player, each of the 6
Due to a manufacturing error, eight cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack.(a) Determine
Suppose there is a 24.4% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 13.9% probability that a randomly selected person aged 40 years or
Determine the probability that at least 2 people in a room of 13 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following
Teen Communication The following data represent the number of different communication activities used by a random sample of teenagers in a given week. Complete parts (a) through (d).(a) Are the
The fixed-price dinner at Mabenka Restaurant provides the following choices:Appetizer: soup or salad Entrée: baked chicken, broiled beef patty, baby beef liver, or roast beef au jus Dessert: ice
The International Air Transport Association (IATA) assigns three-letter codes to represent airport locations. For example, the code for Fort Lauderdale International Airport is FLL. How many
Three members from a 14-member committee are to be randomly selected to serve as chair, vice-chair, and secretary. The first person selected is the chair, the second is the vice-chair, and the third
You have just been hired as a book representative for Pearson Education. On your first day, you must travel to seven schools to introduce yourself. How many different routes are possible?Approach
Evaluate:(a) 7P5(b) 5P5By Hand ApproachTechnology ApproachWe will use a TI-84 Plus C graphing calculator in part (a) and Excel in part (b) to evaluate each permutation. The steps for determining
In how many ways can horses in a ten-horse race finish first, second, and third?Approach The ten horses are distinct. Once a horse crosses the finish line, that horse will not cross the finish line
Roger, Ken, Tom, and Jay are going to play golf. They will randomly select teams of two players each. List all possible team combinations. That is, list all the combinations of the four people Roger,
Evaluate:(a) 4C1(b) 6C4(c) 6C2 By Hand ApproachTechnology Approach We will use a TI-84 Plus C graphing calculator in part (a) and Excel in parts (b) and (c) to evaluate each combination. The steps
How many different simple random samples of size 4 can be obtained from a population whose size is 20?Approach The 20 individuals in the population are distinct. In addition, the order in which
A DNA sequence consists of a series of letters representing a DNA strand that spells out the genetic code. There are four possible letters (A, C, G, and T), each representing a specific nucleotide
How many different vertical arrangements are there of 10 flags if 5 are white, 3 are blue, and 2 are red?Approach Because there are nondistinct items and order matters, use the formula for finding
In the Illinois Lottery, an urn contains balls numbered 1–52. From this urn, six balls are randomly chosen without replacement. For a $$1$ bet, a player chooses two sets of six numbers. To win,
A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The plant’s quality-control manager randomly selects and inspects 5 fasteners. What is the
Rewrite each logarithmic expression as an equivalent exponential expression.Rewrite each exponential expression as an equivalent logarithmic expression.(a) loga 12 = 5 (b) log10 x = 2(c) 4y = 13 (d)
Write each expression as a sum of logarithms. Express powers as factors.(a) loga x2(b) loga(x4y3)(c) loga(4x3)Approach Use Properties (1) and (2).
Evaluate the following expressions. Round your answers to three decimal places.(a) log 4.5(b) 103.4 Approach Use a calculator to evaluate these expressions.
The data in Table 16 represent the temperature of a pizza removed from an oven measured in 5-minute intervals.(a) Draw a scatter diagram of the data treating time, x, as the explanatory
Scott drops a ball from various heights and records the time, x, that it takes for the ball to hit the ground, using a motion detector. He obtains the data displayed in Table 18.(a) Draw a scatter
Is the following a probability model? What do we call the outcome “red”? Color Probability Red 0 Green 0.1 Blue 0.1 Brown 0.3 Yellow 0.15 Orange 0.35
Verify that the following is a probability model. If the model represents the colors of M&Ms in a bag of milk chocolate M&Ms, explain what the model implies. Color Probability Red 0 Green 0
Why is the following not a probability model? Color Probability Red 0.3 Green -0.4 Blue 0.2 Brown 0.4 Yellow 0.2 Orange 0.3
Which of the following numbers could be the probability of an event?0.33, −0.54, 1, 0, 1.16, 0.01
In a certain card game, the probability that a player is dealt a particular hand is 0.48. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand
Suppose you toss a coin 100 times and get 54 heads and 46 tails. Based on these results, what is the probability that the next flip results in a head?
According to a certain country’s education department, 43.6% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
Compute the probability of the event E = {1, 2}.Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event E = “an even number less than 8.”Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event E = “an even number.”Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Planting Tulips A bag of 100 tulip bulbs purchased from a nursery contains 35 red tulip bulbs, 20 yellow tulip bulbs, and 45 purple tulip bulbs.(a) What is the probability that a randomly selected
A police officer randomly selected 555 police records of larceny. The accompanying data represent the number of offenses for various types of larceny.(a) Construct a probability model for type of
Dominique, Marco, and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to
A baseball player hit 69 home runs in a season. Of the 69 home runs, 22 went to right field, 23 went to right center field, 10 went to center field, 12 went to left center field, and 2 went to left
(a) Roll a single die 50 times, recording the result of each roll of the die. Use the results to approximate the probability of rolling a three.(b) Roll a single die 100 times, recording the result
Determine whether the probabilities below are computed using the classical method, empirical method, or subjective method.(a) The probability of having six girls in a six-child family is 0.015625.(b)
In a recent survey, it was found that the median income of families in country A was $$57$,000. What is the probability that a randomly selected family has an income less than $$57$,100?
State the definition of a logarithm.

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