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introduction to statistical investigations

Questions and Answers of Introduction To Statistical Investigations

The 2012 U.S. Pet Ownership and Demographics Sourcebook reported that 36.5% of American households have a pet dog and 30.4% have a pet cat. a. Does it follow from this information that 36.5% +
According to the U.S. Census Bureau, the following table gives the probability distribution that a randomly chosen family household in the United States in 2016 has X members. A family household is
Given that P(A) = 0.80, P(B) = 0.50, and P(A and B) = 0.40, answer the following questions. a. What is P(A|B)? b. What is P(B|A)? c. What is P(A or B)? d. Are events A and B
Calvin is taking a 10-question true/false test and determining which answer to choose for each question by flipping a fair coin. He picks true if he gets heads and false if he gets tails. a.
If adult female guinea pigs weights are normally distributed with a mean of 800 grams and a standard deviation of 100 grams, using the empirical rule, what proportion of adult female guinea pigs
According to the Pew Research Center, in 2015, 58% of all American adults had Facebook accounts. Suppose this is true now. If a random sample of 100 Americans is to be taken, use the normal
Given that P(A) = 0.7, P(B)= 0.2, and P(A and B) = 0, answer the following questions. a. What is P(Ac)? b. What is P(Bc)? c. What is P(A or B)? d. Are events A and B mutually
Suppose that three business executives (call them Abby, Bernice, and Caitlin) drop their cell phones in an elevator and then pick them up at random. a. Write out the sample space of all possible
According to the U.S. Census Bureau, the following table gives the probability distribution that a randomly chosen nonfamily household in the United States in 2016 has Y members. A nonfamily
According to the Pew Research Center, in 2015, 58% of all American adults had Facebook accounts. Suppose this is true now. If a random sample of 100 Americans is to be taken, use the normal
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. Scores on the test that are 130
Suppose you toss three fair coins. a. What is the sample space? is one of the outcomes in the sample space and there are a total of 8 outcomes.) b. All 8 events you listed in part (a) are
Reconsider Exercise 11.1.8 about three business executives dropping their cell phones in an elevator and then picking them up at random. a. Report the probability that exactly one person picks
Suppose that there’s a 20% chance of rain on Saturday. The probabilities for Sunday depend on what happens on Saturday. If it rains on Saturday, then there’s an 80% chance of rain on Sunday and
Suppose you toss three fair coins as described in Exercise 11.3.9. (If you haven’t written out the sample space as described in Exercise 11.3.9, you should do that before answering the following
In Exercise 11.5.7 we looked at the probability distribution of the sum of two dice. This time we focus on using probability rules to derive the properties of the sum of two dice. a. Create a
Suppose that 28% of adults in a certain community have received a speeding ticket, that 42% have received a parking ticket, and that 17% have received both a speeding ticket and a parking ticket.
Suppose you toss three fair coins. a. What is the sample space? is one of the events in the sample space and there are a total of 8 events.) b. All eight events you listed in part (a) are
In 1941, Joe DiMaggio got at least one hit in 56 consecutive games, still the record for the longest hitting streak in Major League Baseball. Let’s try to estimate the probability of someone like
When two distributions are subtracted to form a new distribution, the new distribution must have a standard deviation of zero when which of A–E occur? (Choose all that apply.) A. The
Suppose that a couple has four children. Assume that all 16 outcomes in the sample space are equally likely. a. List the sample space of all possible outcomes for the sexes of these four
Suppose events A and B are independent, P(A) ≠ 0 and P(B) ≠ 0. Can events A and B also be mutually exclusive? Explain.
According to the Census Bureau, 33.4% of Americans 25 years old and older had a college degree (at least a bachelor’s) in 2016. a. If a random sample of 6 American 25 years old and older is
Which is NOT true about probability density functions? A. The total area under the curve of a probability density function and above the horizontal axis is 1. B. Using a probability density
In 2014, the U.S. Census Bureau estimated that 13% of U.S. residents were foreign-born. Suppose this is exactly true. If a random sample of 500 Americans was taken in 2014, use the normal
Which of the following Venn diagrams correctly represents the situation where P(A) = 0.30, P(B) = 0.40, and P(A or B) = 0.60?A.B.C.D.E. 0.20 0.10 0.40 0.30 B
Suppose a fair coin is tossed 3 times and we let X represent the number of coins that land heads up. a. Create a probability distribution for X. b. What does the event X = 2 mean in this
Answer the following yes/no questions about simulation analyses. a. Is it possible to conduct a simulation analysis by hand, without using a computer? b. Are computers generally able to
One way that large families often decide who will give each other Christmas presents is to do a drawing. All the names go in a hat and each person draws a name and that is the person to whom he or
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
In a game we will call “gambling dice,” you pay $1 to roll two dice. If you roll a sum of 5, 6, 7, or 8, you lose and don’t get your dollar back (you are out $1). If you roll anything else, you
About 51% of babies born in the United States are boys. Let’s assume that the probability of a birth resulting in a boy is 0.51 for all U.S. births. Suppose a couple decides they want to have four
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. There are various IQs for which
Use the Random Babies applet to investigate what happens as the number of babies (and mothers) increases. Start with only 2 babies, and then proceed to 4, 6, and 8 babies. For each number, simulate
Recall the probability distribution for family household size given in Exercise 11.4.8. a. What was the mean family household size in the United States in 2016? b. What was the standard
According to the Pew Research Center, in 2015, 19% of all American adults had Twitter accounts. Suppose this is true now. a. If a random sample of 500 Americans is taken, use the normal
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. The wheel is spun and a ball will
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Instagram are shown in the following two-way table. a. Use
Assuming the probability that a family has a boy or a girl is the same (0.50), if a family has three children, what is the probability that: a. The oldest two are girls and the youngest is a
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
What are the mean and standard deviation for the two probability distributions for the number of boys and the number of girls in families of four from Exercise 11.6.10?Data from Exercise 11.6.10About
Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Twitter are shown in the following two-way table. a. What
According to the Pew Research Center, in 2015, 19% of all American adults had Twitter accounts. Suppose this is true now. a. If a random sample of 500 Americans is taken, use the normal
In Exercise 11.2.11, are the events that a randomly chosen person uses Facebook and a randomly chosen person uses Instagram mutually exclusive? What would have to be true about Facebook and Instagram
Repeat Exercise 11.1.10 for the approximate probability that at least one baby is returned to the right mother.Data from Exercise 11.1.10Use the Random Babies applet to investigate what happens as
Repeat Exercise 11.1.10 for the approximate probability that at least one baby is returned to the right mother.Data from Exercise 11.1.10Use the Random Babies applet to investigate what happens as
Recall the probability distribution for nonfamily household size given in Exercise 11.4.9. a. What was the mean nonfamily household size in the United States in 2016? b. What was the
An American roulette wheel has numbers 1 through 36, where the even numbers are black and odd numbers are red. There are also numbers 0 and 00, which are green. Suppose you plan always to bet $1 on
As estimated by the Pew Research in 2016, the probability a randomly chosen American adult uses Instagram is 0.28, the probability a randomly chosen American adult uses Twitter is 0.21, and the
As estimated by the Pew Research Center in 2016, the probabilities associated with a randomly chosen American adult using Facebook and Instagram are shown in the following two-way table. a. Use
Airlines will often overbook their flights (selling more tickets than they have seats) because not all customers show up for some flights. The proportion that doesn’t show up varies greatly,
Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
Recall the probability distribution for the number of people in a family of four who will draw their own name given in Exercise 11.4.10. a. What is the expected value for the number of people
About 20% of the world’s population lives in China. Suppose this is exactly true. a. If a random sample of 1,000 people in the world is chosen, use the normal approximation to the binomial
Recall the scenario of drawing names to decide who would give a Christmas present in a family of four in Exercise 11.4.10. Suppose a family of three uses the same method. a. Create a probability
The SAT® and ACT® are two common standardized tests that high school students take as part of college applications. In 2016 the mean composite SAT score was 1,020 with a standard deviation of 194.
As estimated by the Pew Research Center in 2016, the probability a randomly chosen American adult uses Instagram is 0.28, the probability a randomly chosen American adult uses Twitter is 0.21, and
Results from the Wechsler Adult Intelligence Scale, a common IQ test, are approximately normally distributed with a mean of 100 and a standard deviation of 15. a. If a person is randomly chosen
Recall Exercise 11.5.11 on betting on the number 23 on the roulette wheel. a. Write out the probability distribution for betting $1 on red twice. b. Find the mean of your probability
Random ice cream prices: As in Example 11.1, consider rolling many (fair six-sided) dice, where price is still determined as the largest number followed by the smallest number (in cents). Answer the
The SAT® is a common standardized test that high school students take as part of college entrance. In 2016 the mean composite SAT score was 1020 with a standard deviation of 194. These scores are
A Canadian study (Janssen et al., 2007) looked at the birthweights of babies of different ethnic groups. Their sample of newborns (born after 39 weeks) of European descent had a mean length of 50.5
Birthweights of full-term newborns in the United States are approximately normally distributed with a mean of about 3,500 grams and a standard deviation of about 450 grams. We will assume this is
In Exercise 11.2.13, are the events that a randomly chosen person uses Twitter and a randomly chosen person uses Instagram complements of each other? What would have to be true about Twitter and
Consecutive numbers: a. Determine the (exact, theoretical) probability that rolling a pair of fair six-sided dice results in consecutive numbers, such as (1, 2) or (5, 4).b. Suppose that the
Suppose that a family has three children, and each child is equally likely to be a boy or a girl. a. Write out the sample space of 8 possible outcomes. (For example, use the notation B1G2B3 to
The example in this section described a prize wheel divided into 12 equal-sized sectors where 8 are marked no prize, 3 are marked win $1, and 1 is marked win $25. We will call this wheel A. Suppose
In Exercise 11.3.14, are the events “a randomly chosen person uses Twitter” and “a randomly chosen person uses Instagram” independent? What would have to be true about Twitter and Instagram
In 2014, Jack in the Box® restaurants conducted a game called the Munchie Peel Instant Win Game® where you could peel a sticker off one of their meal boxes and possibly win a prize. They claimed
The ACT® is a common standardized test that high school students take as part of college entrance. In 2016 the mean composite ACT score was 21.0 with a standard deviation of 5.4. These scores are
In 2018, Tim Hortons® restaurants conducted a game called Roll up the Rim to Win® where you could roll up the rim of one of their medium-sized or larger beverage paper cups (to reveal something
About 10% of the population is left-handed. Let’s suppose this is exactly true and you are randomly choosing people from the population until you get a left-hander. a. What is the probability
Repeat Exercise 11.1.11 for the average number of babies that are returned to the right mother.Data from Exercise 11.1.11Repeat Exercise 11.1.10 for the approximate probability that at least one baby
Recall Exercise 11.5.10 on betting on red on the roulette wheel. a. Write out the probability distribution of the payout for betting $1 on red twice. b. Find the mean of your probability
Human blood types can be separated into four categories: A, B, AB, and O. The following partial distribution gives the approximate proportion in which these types occur in the U.S.
According to the Census Bureau, 33.4% of Americans 25 years old and older had a college degree in 2016. a. Use the One Proportion applet to do a simulation (with at least 10,000 repetitions) to
The Canadian study described in Exercise 11.5.14 that looked at the birthweights of babies of different ethnic groups also had a sample of newborns of South Asian descent that had a mean length of
In 2008 a college was shut down because of high rates of norovirus in the student population. The following table gives the numbers of male and female students who did and did not contract the virus
In 2008 a college was shut down because of high rates of norovirus in the student population. The following table gives the numbers of male and female students who did and did not contract the virus
Suppose that a family has four children, and each child is equally likely to be a boy or a girl. a. Write out the sample space of 16 possible outcomes. (For example, use the notation B1G2G3B4 to
Reconsider the prize wheels described in the Example 11.4 and in Exercise 11.4.15. The average distance the outcomes are from the expected value for the wheel from the example (wheel A) can be
In Exercise 11.6.15 about the Munchie Peel Instant Win Game®: a. What is the expected number of winning stickers for those that buy four meals? b. What is the standard deviation for the
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. Heights of females in the United States are
An elevator near the office of one of the authors contains a sign that says its maximum capacity is 4,000 pounds or 26 people. It makes one wonder (well, at least it made one author wonder!), what is
A statistics instructor gave a 10-point quiz in which the mean was 7.72 with a standard deviation of 2.45. Suppose the instructor, being in a generous mood, adjusts all the scores by adding a point
A teacher was on a committee consisting of four male and two female teachers. Two members of the committee were chosen to do some extra work, and it turned out that both females were chosen. The
The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let So represent the event a student chosen is a sophomore and let F represent
Suppose a litter of puppies has 3 males and 3 females. Suppose two puppies are chosen at random and we let X be the number of male puppies chosen. a. Create a probability distribution for
Use data from the table in Exercise 11.2.16 about the norovirus to answer the following questions. a. What is the value of P((Y or F)c) and what does it mean in the context of this
The following two-way table categorizes the class standing at Hope College for males and females in the fall of 2016. Let S represent the event a student chosen is a sophomore and let F represent
Some marathons are so popular that they use lotteries to determine who can run in them. In the 2016 New York City Marathon, about 23% of those who registered to enter through the lottery were
Heights of females in the United States are approximately normally distributed with a mean of 63.8 inches and a standard deviation of 2.8 inches. a. What is the probability that a randomly
A statistics instructor gave a 10-point quiz in which the mean was 8.28 with a standard deviation of 1.58. Suppose the instructor, being a mean ogre, adjusts all the scores by dividing them all by 2
A 19-foot Scout fishing boat contains a U.S. Coast Guard label for maximum capacity. It states that the maximum capacity is 6 persons or 1,000 pounds (not including gear). a. The average weight
Reconsider Exercise 11.1.17. Let’s call the male members of the committee Abe, Bob, Carlos, and Dante. Let’s call the female members Ellen and Fiona. a. List the sample space of all possible
In a certain college statistics class, 61% of the students are female and 39% are male. Of the females, 40% are regular coffee drinkers. Of the males, 30% are regular coffee drinkers. a. What
Suppose you are asked to play a game where you roll a single six-sided die. If it lands on a 6, you win $10. If it doesn’t land on 6, you roll again. If it lands on a 6, the second time you win $6.
In Exercise 11.6.17 about getting into the New York City Marathon: a. What is the mean number of times people get accepted if they enter the lottery for 5 years? b. What is the mean number
Heights of males in the United States are approximately normally distributed with a mean of 69.3 inches and a standard deviation of 3.0 inches. a. What is the probability that a randomly chosen

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